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Books on the topic 'Brownian Motion model'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Wiersema, Ubbo F. Brownian Motion Calculus. New York: John Wiley & Sons, Ltd., 2008.

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2

Wiersema, Ubbo F. Brownian motion calculus. Chichester: John Wiley & Sons, 2008.

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3

Stochastic calculus for fractional Brownian motion and related processes. Berlin: Springer-Verlag, 2008.

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4

Nourdin, Ivan. Selected Aspects of Fractional Brownian Motion. Milano: Springer Milan, 2012.

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5

Jean, Bertoin, Martinelli F, Peres Y, Bernard P. 1944-, Bertoin Jean, Martinelli F, and Peres Y, eds. Lectures on probability theory and statistics: Ecole d'été de probabilités de Saint-Flour XXVII, 1997. Berlin: Springer, 2000.

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6

Ecole d'été de probabilités de Saint-Flour (27th 1997). Lectures on probability theory and statistics: Ecole d'eté de probabilités de Saint-Flour XXVII, 1997. Edited by Bertoin Jean, Martinelli F, Peres Y, and Bernard P. 1944-. Berlin: Springer, 1999.

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7

Quantization in astrophysics, Brownian motion and supersymmetry: Including articles never before published. Chennai, Tamil Nadu: MathTiger, 2007.

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8

Weilin, Xiao, ed. Fen shu Bulang yun dong xia gu ben quan zheng ding jia yan jiu: Mo xing yu can shu gu ji. Beijing: Ke xue chu ban she, 2013.

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9

Froot, Kenneth. Stochastic process switching: Some simple solutions. Cambridge, MA: National Bureau of Economic Research, 1989.

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10

E, Shreve Steven, ed. Methods of mathematical finance. New York: Springer, 1998.

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11

Svensson, Lars E. O. The term structure of interest rate differentials in a target zone: Theory and Swedish data. Cambridge, MA: National Bureau of Economic Research, 1990.

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12

Svensson, Lars E. O. The term structure of interest rate differentials in a target zone: Theory and Swedish data. London: Centre for Economic Policy Research, 1991.

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13

author, Sarich Marco 1985, ed. Metastability and Markov state models in molecular dynamics: Modeling, analysis, algorithmic approaches. Providence, Rhode Island: American Mathematical Society, 2013.

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14

Herrmann, Samuel. Stochastic resonance: A mathematical approach in the small noise limit. Providence, Rhode Island: American Mathematical Society, 2014.

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15

Crossland, Rachel. A Brownian Model for Literary Crowds. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198815976.003.0007.

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Chapter 6 applies the ideas explored in Chapter 5 to a range of early twentieth-century literary texts, especially those by Woolf and Lawrence. The focus here is on crowd and city scenes, including the modernist figures of the flâneur and the passante. The chapter as a whole argues for the relevance of contemporary ideas on molecular physics, especially Brownian motion, to portrayals of individual characters in relation to crowds, drawing on a range of texts including Woolf’s Night and Day and Mrs Dalloway, Lawrence’s The Trespasser and The White Peacock, and texts by Joseph Conrad, James Joyce, and H. G. Wells. Together with Chapter 5, this chapter demonstrates how ideas, language, and imagery were shared across disciplines in the early twentieth century, and argues that considering different disciplines together can help us to recapture a sense of the ways in which particular issues were experienced at the time.

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16

Majumdar, Satya N. Random growth models. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.38.

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This article discusses the connection between a particular class of growth processes and random matrices. It first provides an overview of growth model, focusing on the TASEP (totally asymmetric simple exclusion process) with parallel updating, before explaining how random matrices appear. It then describes multi-matrix models and line ensembles, noting that for curved initial data the spatial statistics for large time t is identical to the family of largest eigenvalues in a Gaussian Unitary Ensemble (GUE multi-matrix model. It also considers the link between the line ensemble and Brownian motion, and whether this persists on Gaussian Orthogonal Ensemble (GOE) matrices by comparing the line ensembles at fixed position for the flat polynuclear growth model (PNG) and at fixed time for GOE Brownian motions. Finally, it examines (directed) last passage percolation and random tiling in relation to growth models.

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17

Brownian Motion Calculus. John Wiley & Sons, 2005.

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18

Its, Alexander R. Random matrix theory and integrable systems. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.10.

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This article discusses the interaction between random matrix theory (RMT) and integrable theory, leading to ordinary and partial differential equations (PDEs) for the eigenvalue distribution of random matrix models of size n and the transition probabilities of non-intersecting Brownian motion models, for finite n and for n → ∞. It first provides an overview of the connection between the theory of orthogonal polynomials and the KP-hierarchy in integrable systems before examining matrix models and the Virasoro constraints. It then considers multiple orthogonal polynomials, taking into account non-intersecting Brownian motions on ℝ (Dyson’s Brownian motions), a moment matrix for several weights, Virasoro constraints, and a PDE for non-intersecting Brownian motions. It also analyses critical diffusions, with particular emphasis on the Airy process, the Pearcey process, and Airy process with wanderers. Finally, it describes the Tacnode process, along with kernels and p-reduced KP-hierarchy.

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19

Bertoin, J., F. Martinelli, and Y. Peres. Lectures on Probability Theory and Statistics: Ecole d'Ete de Probabilites de Saint-Flour XXVII - 1997 (Lecture Notes in Mathematics). Springer, 2000.

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20

Kuijlaars, Arno. Supersymmetry. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.7.

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This article examines conceptual and structural issues related to supersymmetry. It first provides an overview of generating functions before discussing supermathematics, with a focus on Grassmann or anticommuting variables, vectors and matrices, groups and symmetric spaces, and derivatives and integrals. It then considers various applications of supersymmetry to random matrices, such as the representation of the ensemble average and the Hubbard–Stratonovich transformation, along with its generalization and superbosonization. It also describes matrix δ functions and an alternative representation as well as important and technically challenging problems that supersymmetry addresses beyond the invariant and factorizing ensembles. The article concludes with an analysis of the supersymmetric non-linear σ model, Brownian motion in superspace, circular ensembles and the Colour-Flavour-Transformation.

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21

Nourdin, Ivan. Selected Aspects of Fractional Brownian Motion. Springer, 2016.

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22

Nourdin, Ivan. Selected Aspects of Fractional Brownian Motion. Springer, 2012.

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23

Brownian Models Of Performance And Control. Cambridge University Press, 2013.

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24

On Exponential Functionals of Brownian Motion and Related Processes. Springer, 2001.

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25

Succi, Sauro. Stochastic Particle Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0009.

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Dense fluids and liquids molecules are in constant interaction; hence, they do not fit into the Boltzmann’s picture of a clearcut separation between free-streaming and collisional interactions. Since the interactions are soft and do not involve large scattering angles, an effective way of describing dense fluids is to formulate stochastic models of particle motion, as pioneered by Einstein’s theory of Brownian motion and later extended by Paul Langevin. Besides its practical value for the study of the kinetic theory of dense fluids, Brownian motion bears a central place in the historical development of kinetic theory. Among others, it provided conclusive evidence in favor of the atomistic theory of matter. This chapter introduces the basic notions of stochastic dynamics and its connection with other important kinetic equations, primarily the Fokker–Planck equation, which bear a complementary role to the Boltzmann equation in the kinetic theory of dense fluids.

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26

Succi, Sauro. The Fluctuating Lattice Boltzmann. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0030.

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Fluid flow at nanoscopic scales is characterized by the dominance of thermal fluctuations (Brownian motion) versus directed motion. Thus, at variance with Lattice Boltzmann models for macroscopic flows, where statistical fluctuations had to be eliminated as a major cause of inefficiency, at the nanoscale they have to be summoned back. This Chapter illustrates the “nemesis of the fluctuations” and describe the way they have been inserted back within the LB formalism. The result is one of the most active sectors of current Lattice Boltzmann research.

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27

Zocchi, Giovanni. Molecular Machines. Princeton University Press, 2018. http://dx.doi.org/10.23943/princeton/9780691173863.001.0001.

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This book presents a dynamic new approach to the physics of enzymes and DNA from the perspective of materials science. Unified around the concept of molecular deformability—how proteins and DNA stretch, fold, and change shape—the book describes the complex molecules of life from the innovative perspective of materials properties and dynamics, in contrast to structural or purely chemical approaches. It covers a wealth of topics, including nonlinear deformability of enzymes and DNA; the chemo-dynamic cycle of enzymes; supra-molecular constructions with internal stress; nano-rheology and viscoelasticity; and chemical kinetics, Brownian motion, and barrier crossing. Essential reading for researchers in materials science, engineering, and nanotechnology, the book also describes the landmark experiments that have established the materials properties and energy landscape of large biological molecules. The book gives graduate students a working knowledge of model building in statistical mechanics, making it an essential resource for tomorrow's experimentalists in this cutting-edge field. In addition, mathematical methods are introduced in the bio-molecular context. The result is a generalized approach to mathematical problem solving that enables students to apply their findings more broadly.

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28

Furst, Eric M., and Todd M. Squires. Multiple particle tracking. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199655205.003.0004.

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The fundamentals and best practices of multiple particle tracking microrheology are discussed, including methods for producing video microscopy data, analyzing data to obtain mean-squared displacements and displacement correlations, and, critically, the accuracy and errors (static and dynamic) associated with particle tracking. Applications presented include two-point microrheology, methods for characterizing heterogeneous material rheology, and shell models of local (non-continuum) heterogeneity. Particle tracking has a long history. The earliest descriptions of Brownian motion relied on precise observations, and later quantitative measurements, using light microscopy.

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29

Milonni, Peter W. An Introduction to Quantum Optics and Quantum Fluctuations. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199215614.001.0001.

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This book is an introduction to quantum optics for students who have studied electromagnetism and quantum mechanics at an advanced undergraduate or graduate level. It provides detailed expositions of theory with emphasis on general physical principles. Foundational topics in classical and quantum electrodynamics, including the semiclassical theory of atom-field interactions, the quantization of the electromagnetic field in dispersive and dissipative media, uncertainty relations, and spontaneous emission, are addressed in the first half of the book. The second half begins with a chapter on the Jaynes-Cummings model, dressed states, and some distinctly quantum-mechanical features of atom-field interactions, and includes discussion of entanglement, the no-cloning theorem, von Neumann’s proof concerning hidden variable theories, Bell’s theorem, and tests of Bell inequalities. The last two chapters focus on quantum fluctuations and fluctuation-dissipation relations, beginning with Brownian motion, the Fokker-Planck equation, and classical and quantum Langevin equations. Detailed calculations are presented for the laser linewidth, spontaneous emission noise, photon statistics of linear amplifiers and attenuators, and other phenomena. Van der Waals interactions, Casimir forces, the Lifshitz theory of molecular forces between macroscopic media, and the many-body theory of such forces based on dyadic Green functions are analyzed from the perspective of Langevin noise, vacuum field fluctuations, and zero-point energy. There are numerous historical sidelights throughout the book, and approximately seventy exercises.

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30

Crossland, Rachel. Modernist Physics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198815976.001.0001.

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Modernist Physics takes as its focus the ideas associated with three scientific papers published by Albert Einstein in 1905, considering the dissemination of those ideas both within and beyond the scientific field, and exploring the manifestation of similar ideas in the literary works of Virginia Woolf and D. H. Lawrence. Drawing on Gillian Beer’s suggestion that literature and science ‘share the moment’s discourse’, Modernist Physics seeks both to combine and to distinguish between the two standard approaches within the field of literature and science: direct influence and the zeitgeist. The book is divided into three parts, each of which focuses on the ideas associated with one of Einstein’s papers. Part I considers Woolf in relation to Einstein’s paper on light quanta, arguing that questions of duality and complementarity had a wider cultural significance in the early twentieth century than has yet been acknowledged, and suggesting that Woolf can usefully be considered a complementary, rather than a dualistic, writer. Part II looks at Lawrence’s reading of at least one book on relativity in 1921, and his subsequent suggestion in Fantasia of the Unconscious that ‘we are in sad need of a theory of human relativity’—a theory which is shown to be relevant to Lawrence’s writing of relationships both before and after 1921. Part III considers Woolf and Lawrence together alongside late nineteenth- and early twentieth-century discussions of molecular physics and crowd psychology, suggesting that Einstein’s work on Brownian motion provides a useful model for thinking about individual literary characters.

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31

Guionnet, Alice. Free probability. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0003.

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Free probability was introduced by D. Voiculescu as a theory of noncommutative random variables (similar to integration theory) equipped with a notion of freeness very similar to independence. In fact, it is possible in this framework to define the natural ‘free’ counterpart of the central limit theorem, Gaussian distribution, Brownian motion, stochastic differential calculus, entropy, etc. It also appears as the natural setup for studying large random matrices as their size goes to infinity and hence is central in the study of random matrices as their size go to infinity. In this chapter the free probability framework is introduced, and it is shown how it naturally shows up in the random matrices asymptotics via the so-called ‘asymptotic freeness’. The connection with combinatorics and the enumeration of planar maps, including loop models, are discussed.

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32

Methods of Mathematical Finance. Springer, 2015.

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33

Karatzas, Ioannis, and Steven Shreve. Methods of Mathematical Finance. Springer, 2016.

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34

Shreve, Steven E., and Ioannis Karatzas. Methods of Mathematical Finance. Springer, 2001.

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35

Methods of Mathematical Finance. Springer, 2016.

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