Relevant bibliographies by topics / Product of random matrices

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  2. Dissertations / Theses
  3. Books
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Academic literature on the topic 'Product of random matrices'

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Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Product of random matrices"

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Touri, Behrouz, and Angelia Nedic. "Product of Random Stochastic Matrices." IEEE Transactions on Automatic Control 59, no. 2 (February 2014): 437–48. http://dx.doi.org/10.1109/tac.2013.2283750.

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TKOCZ, TOMASZ, MAREK SMACZYŃSKI, MAREK KUŚ, OFER ZEITOUNI, and KAROL ŻYCZKOWSKI. "TENSOR PRODUCTS OF RANDOM UNITARY MATRICES." Random Matrices: Theory and Applications 01, no. 04 (October 2012): 1250009. http://dx.doi.org/10.1142/s2010326312500098.

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Tensor products of M random unitary matrices of size N from the circular unitary ensemble are investigated. We show that the spectral statistics of the tensor product of random matrices becomes Poissonian if M = 2, N become large or M become large and N = 2.
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Berger, Marc A. "A trotter product formula for random matrices." Stochastics 23, no. 2 (February 1988): 79–84. http://dx.doi.org/10.1080/17442508808833483.

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CHENG, XIUYUAN, and AMIT SINGER. "THE SPECTRUM OF RANDOM INNER-PRODUCT KERNEL MATRICES." Random Matrices: Theory and Applications 02, no. 04 (October 2013): 1350010. http://dx.doi.org/10.1142/s201032631350010x.

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We consider n × n matrices whose (i, j)th entry is [Formula: see text], where X1, …, Xn are i.i.d. standard Gaussian in ℝp, and f is a real-valued function. The weak limit of the eigenvalue distribution of these random matrices is studied at the limit when p, n → ∞ and p/n = γ which is a constant. We show that, under certain conditions on the kernel function f, the limiting spectral density exists and is dictated by a cubic equation involving its Stieltjes transform. The parameters of this cubic equation are decided by a Hermite-like expansion of the rescaled kernel function. While the case that f is differentiable at the origin has been previously resolved by El Karoui [The spectrum of kernel random matrices, Ann. Statist.38 (2010) 1–50], our result is applicable to non-smooth f, such as the Sign function and the hard thresholding operator of sample covariance matrices. For this larger class of kernel functions, we obtain a new family of limiting densities, which includes the Marčenko–Pastur (M.P.) distribution and Wigner's semi-circle distribution as special cases.
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Deutsch, J. M., and G. Paladin. "Product of Random Matrices in a Microcanonical Ensemble." Physical Review Letters 62, no. 7 (February 13, 1989): 695–99. http://dx.doi.org/10.1103/physrevlett.62.695.

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Gol'dsheid, I. Ya, and G. A. Margulis. "Lyapunov indices of a product of random matrices." Russian Mathematical Surveys 44, no. 5 (October 31, 1989): 11–71. http://dx.doi.org/10.1070/rm1989v044n05abeh002214.

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Rogers, Tim. "Universal sum and product rules for random matrices." Journal of Mathematical Physics 51, no. 9 (September 2010): 093304. http://dx.doi.org/10.1063/1.3481569.

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Bose, Arup, and Soumendu Sundar Mukherjee. "Bulk behavior of Schur–Hadamard products of symmetric random matrices." Random Matrices: Theory and Applications 03, no. 02 (April 2014): 1450007. http://dx.doi.org/10.1142/s2010326314500075.

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We develop a general method for establishing the existence of the Limiting Spectral Distributions (LSD) of Schur–Hadamard products of independent symmetric patterned random matrices. We apply this method to show that the LSD of Schur–Hadamard products of some common patterned matrices exist and identify the limits. In particular, the Schur–Hadamard product of independent Toeplitz and Hankel matrices has the semi-circular LSD. We also prove an invariance theorem that may be used to find the LSD in many examples.
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Borodin, Alexei, Vadim Gorin, and Eugene Strahov. "Product Matrix Processes as Limits of Random Plane Partitions." International Mathematics Research Notices 2020, no. 20 (January 16, 2019): 6713–68. http://dx.doi.org/10.1093/imrn/rny297.

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AbstractWe consider a random process with discrete time formed by squared singular values of products of truncations of Haar-distributed unitary matrices. We show that this process can be understood as a scaling limit of the Schur process, which gives determinantal formulas for (dynamical) correlation functions and a contour integral representation for the correlation kernel. The relation with the Schur processes implies that the continuous limit of marginals for q-distributed plane partitions coincides with the joint law of squared singular values for products of truncations of Haar-distributed random unitary matrices. We provide structural reasons for this coincidence that may also extend to other classes of random matrices.
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Wang, X. R. "Asymptotic results on the product of random probability matrices." Journal of Physics A: Mathematical and General 29, no. 12 (June 21, 1996): 3053–61. http://dx.doi.org/10.1088/0305-4470/29/12/013.

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Dissertations / Theses on the topic "Product of random matrices"

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ORABY, TAMER. "Spectra of Random Block-Matrices and Products of Random Matrices." University of Cincinnati / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1209391815.

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Kong, Nayeong. "Convergence Rates of Spectral Distribution of Random Inner Product Kernel Matrices." Diss., Temple University Libraries, 2018. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/498132.

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Mathematics
Ph.D.
This dissertation has two parts. In the first part, we focus on random inner product kernel matrices. Under various assumptions, many authors have proved that the limiting empirical spectral distribution (ESD) of such matrices A converges to the Marchenko- Pastur distribution. Here, we establish the corresponding rate of convergence. The strategy is as follows. First, we show that for z = u + iv ∈ C, v > 0, the distance between the Stieltjes transform m_A (z) of ESD of matrix A and Machenko-Pastur distribution m(z) is of order O (log n \ nv). Next, we prove the Kolmogorov distance between ESD of matrix A and Marchenko-Pastur distribution is of order O(3\log n\n). It is the less sharp rate for much more general class of matrices. This uses a Berry-Esseen type bound that has been employed for similar purposes for other families of random matrices. In the second part, random geometric graphs on the unit sphere are considered. Observing that adjacency matrices of these graphs can be thought of as random inner product matrices, we are able to use an idea of Cheng-Singer to establish the limiting for the ESD of these adjacency matrices.
Temple University--Theses
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Cureg, Edgardo S. "Some problems on products of random matrices." [Tampa, Fla] : University of South Florida, 2006. http://purl.fcla.edu/usf/dc/et/SFE0001831.

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Bui, Thi Thuy. "Limit theorems for branching random walks and products of random matrices." Thesis, Lorient, 2020. https://tel.archives-ouvertes.fr/tel-03261556.

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L’objectif du sujet de ma thèse est d’établir des théorèmes limites pour des marches aléatoires avec branchement gouvernées par des produits de matrices aléatoires, en profitant des progrès récents sur les produits de matrices aléatoires et en y établissant de nouveaux résultats adaptés au besoin. La première partie concerne le modèle classique d'une marche aléatoire avec branchement sur la droite réelle. Nous établissons une borne Berry-Esseen et une asymptotique précise de déviation modérée de type Cramér pour la mesure de comptage qui compte le nombre de particules de n-ième génération situées dans une région donnée. La deuxième partie est consacrée à l'étude des produits $G_n = A_n \ldots A_1$ de matrices aléatoires réelles $A_i$ de type $d \times d$, indépendantes et identiquement distribuées. Dans cette partie, avec une motivation pour des applications aux marches aléatoires avec branchement gouvernées par des produits de matrices aléatoires, nous améliorons et étendons le théorème central limite et le théorème limite local établis par Le Page (1982). Dans la troisième partie, on considère un modèle de marches aléatoires avec branchement, où les mouvements des individus sont gouvernés par des produits de matrices aléatoires de type $d \times d$. A l'aide des résultats établis à la deuxième partie pour les produits de matrices aléatoires, on établit un théorème central limite et une expansion asymptotique à grande déviation de type Bahadur-Rao pour la mesure de comptage $ Z_n^x $ qui compte le nombre de particules de n-ième génération situées dans une région donnée avec normalisation appropriée. La quatrième partie est une suite de la troisième partie. Dans cette partie, on établit la borne de type Berry-Esseen à propos de la vitesse de convergence dans le théorème central limite et une asymptotique précise de déviation modérée de type Cramér pour $ Z_n^x $
The main objective of my thesis is to establish limit theorems for a branching random walk with products of random matrices by taking advantage of recent advances in products of random matrices and establishing new results as needed. The first part concerns the classic branching random walk on the real line. We establish a Berry- Esseen bound and a Cramér type moderate deviation expansion for the counting measure which counts the number of particles of nth generation situated in a given region. The second part is devoted to the study of the products $G_n = A_n \ldots A_1$ of real random matrices $A_i$ of type $ d \times d$, independent and identically distributed. In this part, with a motivation for applications to branching random walks governed by products of random matrices, we improve and extend the central limit theorem and the local limit theorem established by Le Page (1982). In the third part, we consider a branching random walk model, where the movements of individuals are governed by products of random matrices of type $ d \times d $. Using the results established in the second part for the products of random matrices, we establish a central limit theorem and a large deviation asymptotic expansion of the Bahadur-Rao type for the counting measure $ Z_n^x $ which counts the number n-th generation particles located in a given region with suitable norming. The fourth part is a continuation of the third part. In this part, we establish the Berry-Esseen bound which gives the speed of convergence in the central limit theorem and a precise Cramér- type moderate deviation asymptotic for $ Z_n^x $
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Ipsen, Jesper R. [Verfasser]. "Products of independent Gaussian random matrices / Jesper R. Ipsen." Bielefeld : Universitätsbibliothek Bielefeld, 2015. http://d-nb.info/1077063482/34.

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Sert, Cagri. "Joint Spectrum and Large Deviation Principles for Random Products of Matrices." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS500/document.

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Après une introduction générale et la présentation d'un exemple explicite dans le chapitre 1, nous exposons certains outils et techniques généraux dans le chapitre 2.- dans le chapitre 3, nous démontrons l'existence d'un principe de grandes déviations (PGD) pour les composantes de Cartan le long des marches aléatoires sur les groupes linéaires semi -simples G. L'hypothèse principale porte sur le support S de la mesure de la probabilité en question et demande que S engendre un semi-groupe Zariski dense. - Dans le chapitre 4, nous introduisons un objet limite (une partie de la chambre de Weyl) que l'on associe à une partie bornée S de G et que nous appelons le spectre joint J(S) de S. Nous étudions ses propriétés et démontrons que J(S) est une partie convexe compacte d'intérieur non-vide dès que S engendre un semi -groupe Zariski dense. Nous relions le spectre joint avec la notion classique du rayon spectral joint et la fonction de taux du PGD pour les marches aléatoires. - Dans le chapitre 5, nous introduisons une fonction de comptage exponentiel pour un S fini dans G, nous étudions ses propriétés que nous relions avec J(S) et démontrons un théorème de croissance exponentielle dense. - Dans le chapitre 6, nous démontrons le PGD pour les composantes d'Iwasawa le long des marches aléatoires sur G. L'hypothèse principale demande l'absolue continuité de la mesure de probabilité par rapport à la mesure de Haar.- Dans le chapitre 7, nous développons des outils pour aborder une question de Breuillard sur la rigidité du rayon spectral d'une marche aléatoire sur le groupe libre. Nous y démontrons un résultat de rigidité géométrique
After giving a detailed introduction andthe presentation of an explicit example to illustrateour study in Chapter 1, we exhibit some general toolsand techniques in Chapter 2. Subsequently,- In Chapter 3, we prove the existence of a large deviationprinciple (LDP) with a convex rate function, forthe Cartan components of the random walks on linearsemisimple groups G. The main hypothesis is onthe support S of the probability measure in question,and asks S to generate a Zariski dense semigroup.- In Chapter 4, we introduce a limit object (a subsetof the Weyl chamber) that we associate to a boundedsubset S of G. We call this the joint spectrum J(S)of S. We study its properties and show that for asubset S generating a Zariski dense semigroup, J(S)is convex body, i.e. a convex compact subset of nonemptyinterior. We relate the joint spectrum withthe classical notion of joint spectral radius and therate function of LDP for random walks on G.- In Chapter 5, we introduce an exponential countingfunction for a nite S in G. We study its properties,relate it to joint spectrum of S and prove a denseexponential growth theorem.- In Chapter 6, we prove the existence of an LDPfor Iwasawa components of random walks on G. Thehypothesis asks for a condition of absolute continuityof the probability measure with respect to the Haarmeasure.- In Chapter 7, we develop some tools to tackle aquestion of Breuillard on the rigidity of spectral radiusof a random walk on a free group. We prove aweaker geometric rigidity result
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Havret, Benjamin. "On the Lyapunov exponent of random transfer matrices and on pinning models with constraints." Thesis, Université de Paris (2019-....), 2019. http://www.theses.fr/2019UNIP7124.

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Cette thèse se divise en deux parties indépendantes. La première (Chapitres 1 et 2) est consacrée à l’analyse de l’exposant de Lyapunov d’un produit de matrices de transfert aléatoires. Cet exposant de Lyapunov apparait de multiples fois dans la littérature physique, notamment dans l’analyse du modèle d’Ising dans certains milieux aléatoires. Nous nous intéressons à une prédiction de la littérature physique concernant son comportement singulier et nous proposons une analyse mathématique de cette singularité. La seconde partie (Chapitres 3, 4 et 5) porte sur une variation du modèle de Poland-Scheraga pour la dénaturation de l’ADN. Cette variation vise la prise en compte des contraintes géométriques particulières des chaines d’ADN circulaires. Nous analysons entièrement le modèle homogène: la régularité et le comportement critique de son énergie libre, ainsi que les trajectoires du polymère. Nous nous intéressons enfin au modèle désordonné, pour lequel nous établissons la pertinence du désordre, tant au niveau de l’énergie libre que des trajectoires du système
This work is made of two independent parts. The first (Chapters 1 and 2) is devoted to the study of the Lyapunov exponent of a product of random transfer matrices. This Lyapunov exponent appears repeatedly in the statistical mechanics literature, notably in the analysis of the Ising model in some special disordered environments. The focus is on a singular behaviour that has been pointed out in the physical literature: we provide a mathematical analysis of this singularity. In the second part (Chapters 3, 4 and 5) we consider a variation of the Poland-Scheraga model for DNA denaturation. This variation aims at modeling the case of circular DNA. We provide a complete analysis of the homogeneous model, including free energy regularity and critical behaviour, as well as path properties. We also tackle the disordered case, for which we prove relevance of disorder both for the free energy and the trajectories of the system
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Jalowy, Jonas [Verfasser]. "Rate of convergence for non-Hermitian random matrices and their products / Jonas Jalowy." Bielefeld : Universitätsbibliothek Bielefeld, 2020. http://d-nb.info/1211475107/34.

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Maquera, Herbert Milton Ccalle. "Teorema de Furstenberg sobre o produto aleatório de matrizes." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-30102018-095453/.

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Nesta dissertação estudamos de um ponto de vista probabilístico, o comportamento assintótico de sistemas dinâmicos. Um exemplo simples de formular e profundo é o estudo de produto aleatório de matrizes (FURSTENBERG; KESTEN, 1960). Utilizaremos como ferramenta o estudo dos cociclos lineares, posteriormente mediante o Teorema de Furstenberg-Kesten definiremos o expoente de Lyapunov do cociclo, em seguida enunciamos e provamos o Teorema Ergódico Multiplicativo de Oseledets o qual nos permite entender o comportamento das órbitas típicas para um cociclo dado F : M x R2 → M x R2. O Teorema de Fusrtenberg-Kesten fornece informações sobre o crescimento das matrizes An(x), enquanto o Teorema de Oseledets descreve o comportamento assintótico dos vetores An(x).v. Finalmente provamos o teorema principal desta dissertação, o Teorema de Furstenberg o qual diz que na maioria dos casos o maior expoente de Lyapunov é positivo (FURSTENBERG, 1963).
In this thesis we study from a probabilistic point of view, the asymptotic behavior of dynamic systems, a deep and simple example is the random product of matrices (FURSTENBERG; KESTEN, 1960). We will use as a tool, the study of linear cocycles, later using the Furstenberg- Kesten Theorem we will define the Lyapunov exponent of the cocycle, then we enunciate and prove the Multiplicative Ergodic Theorem of Oseledets which allow us to understand the behavior of the typical orbits for a given cocycle F : M x R2 → M x R2. The Fusrtenberg- Kesten theorem provides information on the growth of the matrices A(x), while the theorems of Oseledets describe the asymptotic behavior of the vectors An(x).v. Finally we prove our main theorem, Furstenbergs Theorem which states that in most cases the greatest exponent of Lyapunov is positive (FURSTENBERG, 1963).
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Xiao, Hui. "Grandes déviations pour les produits de matrices aléatoires." Thesis, Lorient, 2020. http://www.theses.fr/2020LORIS559.

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L'objet de cette thèse est d'étudier les asymptotiques précises de grandes déviations et de déviations modérées pour les produits de matrices aléatoires indépendantes et identiquement distribuées. Dans la première partie, nous établissons des asymptotiques exactes de types Bahadur-Rao et Petrov pour les probabilités de grandes déviations pour le cocycle de la norme, «dollard»\log|G_nx|»dollard», où «dollard»G_n=g_n\ldots g_1»dollard» est le produit des matrices aléatoires «dollard»g_i»dollard», de type «dollard»d \times d»dollard», indépendantes et identiquement distribuées, «dollard»x»dollard» est un vecteur unitaire de «dollard»\mathbb R^d»dollard». La deuxième partie est consacrée à l'établissement des résultats de grandes déviations de types Bahadur- Rao et Petrov pour les entrées «dollard»(i,j)»dollard»-ème «dollard»G_n^{i,j}»dollard» de «dollard»G_n»dollard». En particulier, notre résultat améliore de manière significative les bornes de grandes déviations établies récemment dans la littérature. Dans la troisième partie, nous obtenons la borne de Berry-Esseen et le développement asymptotique de déviations modérées de type Cramér pour le cocycle de la norme des produits de matrices aléatoires. Ces résultats sont prouvés en élaborant une nouvelle approche basée sur une inégalité de lissage dans le plan complexe et sur la méthode du point-selle. La quatrième partie est consacrée à l'étude des bornes de type Berry-Esseen et au développement asymptotique de déviations modérées de type Cramér pour la norme d'opérateur «dollard»\|G_n\|»dollard», pour les entrées «dollard»G_n^{i,j}»dollard» et le rayon spectral «dollard»\rho(G_n)»dollard» des produits de matrices aléatoires positives. Dans la cinquième partie, nous étudions les bornes de type Berry-Esseen et les principes de déviations modérées pour la norme d'opérateur «dollard»\|G_n\|»dollard» et le rayon spectral «dollard»\rho(G_n)»dollard», pour les matrices inversibles. Nous prouvons également des développements asymptotiques de déviations modérées dans la zone normale «dollard»[0, o (n^{1/6})]»dollard». La sixième partie est consacrée au développement asymptotique de déviation modérée de type Cramér pour les entrées «dollard»G_n^{i,j} «dollard» des produits de matrices aléatoires inversibles
The purpose of this Ph.D. thesis is to study precise large and moderate deviation asymptotics for products of independent and identically distributed random matrices. In the first part, we establish Bahadur-Rao type and Petrov type exact asymptotics of large deviation probabilities for the norm cocycle «dollard»\log|G_nx|»dollard», where «dollard»G_n = g_n\ldots g_1»dollard» is the product of independent and identically distributed random «dollard»d\times d»dollard» matrices «dollard»g_i»dollard», «dollard»x»dollard» is a unit vector in «dollard»\mathbb R^d»dollard». The second part is devoted to establishing Bahadur-Rao type and Petrov type large deviations for the «dollard»(i,j)»dollard»-th entries «dollard»G_n^{i,j}»dollard» of «dollard»G_n»dollard». In particular, our result improves significantly the large deviation bounds established recently. In the third part, we investigate the Berry-Esseen bound and Cramér type moderate deviation expansion for the norm cocycle of products of random matrices. These results are proved by elaborating a new approach based on a smoothing inequality in the complex plane and on the saddle point method. The fourth part is devoted to studying Berry-Esseen bounds and Cramér type moderate deviation expansions for the operator norm «dollard»\|G_n\|»dollard», the entries «dollard»G_n^{i,j}»dollard» and the spectral radius «dollard»\rho(G_n)»dollard», for positive matrices. In the fifth part, we study the Berry-Esseen type bounds and moderate deviation principles for the operator norm «dollard»\|G_n\|»dollard» and the spectral radius «dollard»\rho(G_n)»dollard», for invertible matrices. We also prove the moderate deviation expansions in the normal range «dollard»[0, o(n^{1/6})]»dollard». The sixth part is devoted to the Cramér type moderate deviation expansion for the entries «dollard»G_n^{i,j}»dollard» of products of invertible matrices
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Books on the topic "Product of random matrices"

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Crisanti, Andrea, Giovanni Paladin, and Angelo Vulpiani. Products of Random Matrices. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-84942-8.

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Touri, Behrouz. Product of Random Stochastic Matrices and Distributed Averaging. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28003-0.

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Touri, Behrouz. Product of Random Stochastic Matrices and Distributed Averaging. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Crisanti, Andrea. Products of random matrices in statistical physics. Berlin: Springer, 1993.

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Crisanti, A. Products of random matrices in statistical physics. Berlin: Springer-Verlag, 1993.

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Högnäs, Göran. Probability measures on semigroups: Convolution products, random walks, and random matrices. New York: Plenum Press, 1995.

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1944-, Lacroix Jean, ed. Products of random matrices with applications to Schrödinger operators. Boston: Birkhäuser, 1985.

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Bougerol, Philippe, and Jean Lacroix, eds. Products of Random Matrices with Applications to Schrödinger Operators. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4684-9172-2.

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Voiculescu, D. V. Free random variables: A noncommutative probability approach to free products with applications to random matrices, operator algebras, and harmonic analysis on free groups. Providence, R.I., USA: American Mathematical Society, 1992.

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Random matrices. 3rd ed. Amsterdam: Elsevier/Academic Press, 2004.

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Book chapters on the topic "Product of random matrices"

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Bai, Zhidong, and Jack W. Silverstein. "Product of Two Random Matrices." In Springer Series in Statistics, 59–89. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-0661-8_4.

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Carmona, René, and Jean Lacroix. "Products of Random Matrices." In Spectral Theory of Random Schrödinger Operators, 175–240. Boston, MA: Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4612-4488-2_4.

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Touri, Behrouz. "Ergodicity of Random Chains." In Product of Random Stochastic Matrices and Distributed Averaging, 23–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28003-0_3.

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Touri, Behrouz. "Products of Stochastic Matrices and Averaging Dynamics." In Product of Random Stochastic Matrices and Distributed Averaging, 15–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28003-0_2.

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Touri, Behrouz. "Introduction." In Product of Random Stochastic Matrices and Distributed Averaging, 1–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28003-0_1.

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Touri, Behrouz. "Infinite Flow Stability." In Product of Random Stochastic Matrices and Distributed Averaging, 35–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28003-0_4.

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Touri, Behrouz. "Implications." In Product of Random Stochastic Matrices and Distributed Averaging, 65–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28003-0_5.

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Touri, Behrouz. "Absolute Infinite Flow Property." In Product of Random Stochastic Matrices and Distributed Averaging, 93–112. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28003-0_6.

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Touri, Behrouz. "Averaging Dynamics in General State Spaces." In Product of Random Stochastic Matrices and Distributed Averaging, 113–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28003-0_7.

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Touri, Behrouz. "Conclusion and Suggestions for Future Works." In Product of Random Stochastic Matrices and Distributed Averaging, 127–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28003-0_8.

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Conference papers on the topic "Product of random matrices"

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Babadi, Behtash, and Vahid Tarokh. "Spectral distribution of the product of two random matrices based on binary block codes." In 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2011. http://dx.doi.org/10.1109/allerton.2011.6120264.

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To, C. W. S., and B. Wang. "Response Analysis of Discretized Plates Under In-Plane and External Nonstationary Random Excitations." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0091.

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Abstract Responses of panel structures on board ships and aerospace systems under point and in-plane intensive transient excitations, originating, primarily, from near-mixed explosion and impact upon the ships are investigated and presented in this paper. The panel structures are idealized by finite elements while the intensive transient in-plane and point loads are modelled as nonstationary random processes. The latter are treated as products of modulating functions and Gaussian white noise processes. The focus of the paper is the comparison of results obtained by employing the three nodes, eighteen degree-of-freedoms (DOF) triangular bending plate element (the explicit element stiffness, mass and stability matrices of which have been derived by the authors) and the four nodes, twelve DOF Melosh-Zienkiewicz-Cheung (MZC) rectangular bending plate element. The isssues addressed are: (a) convergence and reduction of computational time by applying the eighteen DOF plate element in comparison to the MZC element, (b) the contribution of the in-plane nonstationary random excitation on the response of the discretized structures, and (c) the influence of the number of modes included in the response computation.
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Karadeniz, H. "Spectral Analysis of Deteriorated Offshore Structures." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43889.

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In order to present an efficient, practical technique to determine progressive failure mechanism of structures, modelling of member deterioration by using a spring system is outlined. The procedure uses updates of member stiffness and mass matrices as well as the random load vector in incremental forms. In this procedure, the assembly process produces redistributions of the system stiffness and mass matrices, and the load vector. In the calculation of response spectral values, the original forms remain unchanged. Inversion of the stiffness matrix is calculated by using the Neumann expansion solution in which the original stiffness matrix is inverted only once so that a considerable computation time is saved in the whole calculation process. An incremental solution technique is presented for spectral analyses of both static and dynamic sensitive structures. In the case of dynamic analysis, special attention is paid to estimations of modified natural frequencies and mode shapes of deteriorated structures, which may affect response spectral values considerably. The technique, which is presented in the paper, is attractive in practical applications and can be efficiently used in the reliability calculation as well, and also it can be successfully used to determine a progressive failure mechanism of the structure.
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BOURGADE, PAUL. "RANDOM BAND MATRICES." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0159.

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Arlitt, Ryan, Anthony Nix, and Rob Stone. "Evaluating TRIZ as a Provider of Provocative Stimuli." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89500.

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The Theory of Inventive Problem Solving (known by its Russian acronym TRIZ) is used across the globe to help engineers working on product design and development. In previous papers the authors developed a Function-Based TRIZ method and began a validation process. A single innovative feature was identified in a sample of innovative products, and these features were traced backwards on the Function-Based TRIZ matrix. The Function-Based TRIZ matrix was deemed successful in cases where any inventive principle suggested by the matrix could have produced the innovative feature. During this process, the authors observed that no matter which principle was used, some mental leap was needed to apply it. Additionally, many different inventive principles can lead to the same concept. This paper examines a new hypothesis: that the provocative stimulus presented by any randomly selected inventive principle facilitates concept generation just as effectively as using the historical contradiction matrix to guide inventive principle selection. This paper presents a study on the benefits of using the TRIZ contradiction matrix to select the “correct” principles during concept generation. During this study, participants were asked to come up with concepts using one of two TRIZ matrices: the real one that contains historical knowledge from an extensive patent search, or a randomly populated one. The results of this exercise were then examined using modified versions of two concept evaluation metrics set forth by Shah: quantity and variety. This paper offers two contributions to the field. The first is a step toward understanding the role and importance of conflict mappings in TRIZ and TRIZ-like problem-solving methodologies. The second is a method for evaluating process variety (as opposed to outcome variety) when TRIZ is used to generate ideas.
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EL KAROUI, NOUREDDINE. "RANDOM MATRICES AND HIGH-DIMENSIONAL STATISTICS: BEYOND COVARIANCE MATRICES." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0163.

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Soloveychik, Ilya, Yu Xiang, and Vahid Tarokh. "Explicit symmetric pseudo-random matrices." In 2017 IEEE Information Theory Workshop (ITW). IEEE, 2017. http://dx.doi.org/10.1109/itw.2017.8277999.

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Vu, V. H. "Spectral norm of random matrices." In the thirty-seventh annual ACM symposium. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1060590.1060654.

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Tao, Terence, and Van Vu. "On random pm 1 matrices." In the thirty-seventh annual ACM symposium. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1060590.1060655.

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ERDŐS, LÁSZLÓ. "UNIVERSALITY OF WIGNER RANDOM MATRICES." In XVIth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814304634_0004.

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Reports on the topic "Product of random matrices"

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Holmes, Robert B. On Random Correlation Matrices. Fort Belvoir, VA: Defense Technical Information Center, October 1988. http://dx.doi.org/10.21236/ada202786.

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Holmes, R. B. On Random Correlation Matrices. 2. The Toeplitz Case. Fort Belvoir, VA: Defense Technical Information Center, March 1989. http://dx.doi.org/10.21236/ada208229.

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Ballard, Grey, Aydin Buluc, James Demmel, Laura Grigori, Benjamin Lipshitz, Oded Schwartz, and Sivan Toledo. Communication Optimal Parallel Multiplication of Sparse Random Matrices. Fort Belvoir, VA: Defense Technical Information Center, February 2013. http://dx.doi.org/10.21236/ada580140.

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Tropp, Joel A. User-Friendly Tools for Random Matrices: An Introduction. Fort Belvoir, VA: Defense Technical Information Center, December 2012. http://dx.doi.org/10.21236/ada576100.

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Vu, Van H. Random Matrices, Combinatorics, Numerical Linear Algebra and Complex Networks. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada567088.

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Pfander, Goetz E., Holger Rauhut, and Joel A. Tropp. The Restricted Isometry Property for Time-Frequency Structured Random Matrices. Fort Belvoir, VA: Defense Technical Information Center, June 2011. http://dx.doi.org/10.21236/ada563016.

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Gittens, Alex, and Joel A. Tropp. Tail Bounds for All Eigenvalues of a Sum of Random Matrices. Fort Belvoir, VA: Defense Technical Information Center, July 2011. http://dx.doi.org/10.21236/ada563094.

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Avram, Florin. On Bilinear Forms in Gaussian Random Variables, Toeplitz Matrices and Parseval's Relation. Fort Belvoir, VA: Defense Technical Information Center, November 1986. http://dx.doi.org/10.21236/ada177100.

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Hribar, M. E., and T. D. Plantenga. Preconditioning a product of matrices arising in trust region subproblems. Office of Scientific and Technical Information (OSTI), March 1996. http://dx.doi.org/10.2172/221914.

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Bai, Z. D., P. R. Krishnaiah, and L. C. Zhao. On the Asymptotic Joint Distributions of the Eigenvalues of Random Matrices Which Arise under Components of Covariance Model. Fort Belvoir, VA: Defense Technical Information Center, June 1987. http://dx.doi.org/10.21236/ada186387.

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