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Journal articles on the topic 'Tracy-Widom'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Su, Zhong-gen, Yu-huan Lei, and Tian Shen. "Tracy-Widom distribution, Airy2 process and its sample path properties." Applied Mathematics-A Journal of Chinese Universities 36, no. 1 (2021): 128–58. http://dx.doi.org/10.1007/s11766-021-4251-2.

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AbstractTracy-Widom distribution was first discovered in the study of largest eigenvalues of high dimensional Gaussian unitary ensembles (GUE), and since then it has appeared in a number of apparently distinct research fields. It is believed that Tracy-Widom distribution have a universal feature like classic normal distribution. Airy2 process is defined through finite dimensional distributions with Tracy-Widom distribution as its marginal distributions. In this introductory survey, we will briefly review some basic notions, intuitive background and fundamental properties concerning Tracy-Widom

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2

Blower, Gordon, and Andrew McCafferty. "Discrete Tracy–Widom operators." Proceedings of the Edinburgh Mathematical Society 52, no. 3 (2009): 545–59. http://dx.doi.org/10.1017/s001309150700140x.

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AbstractIntegrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. We consider discrete Tracy–Widom operators and give sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kernel and kernels arising from the almost Mathieu equation and the Fourier transform of Mathieu's equation.

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3

Allez, Romain, and Laure Dumaz. "Tracy–Widom at High Temperature." Journal of Statistical Physics 156, no. 6 (2014): 1146–83. http://dx.doi.org/10.1007/s10955-014-1058-z.

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4

Johansson, K. "From Gumbel to Tracy-Widom." Probability Theory and Related Fields 138, no. 1-2 (2006): 75–112. http://dx.doi.org/10.1007/s00440-006-0012-7.

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5

Ferrari, Patrik L., and Bálint Vető. "Tracy–Widom asymptotics for $q$-TASEP." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 51, no. 4 (2015): 1465–85. http://dx.doi.org/10.1214/14-aihp614.

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6

Bao, Zhigang. "Tracy–Widom limit for Kendall’s tau." Annals of Statistics 47, no. 6 (2019): 3504–32. http://dx.doi.org/10.1214/18-aos1786.

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7

Domínguez-Molina, J. Armando. "The Tracy–Widom distribution is not infinitely divisible." Statistics & Probability Letters 123 (April 2017): 56–60. http://dx.doi.org/10.1016/j.spl.2016.11.029.

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8

Kotowski, Marcin, and Bálint Virág. "Tracy–Widom Fluctuations in 2D Random Schrödinger Operators." Communications in Mathematical Physics 370, no. 3 (2019): 873–93. http://dx.doi.org/10.1007/s00220-019-03434-3.

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9

Gelbaum, Zachary. "On the largest eigenvalue of products from the β-Laguerre ensemble". Random Matrices: Theory and Applications 03, № 02 (2014): 1450008. http://dx.doi.org/10.1142/s2010326314500087.

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We determine the limiting distribution of the largest eigenvalue of products from the β-Laguerre ensemble. This limiting distribution is given by a Tracy–Widom law with parameter β0 > 0 depending on the ratio of the parameters of the two matrices involved.

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10

Dehaye, Paul-Olivier. "On an Identity due to Bump and Diaconis, and Tracy and Widom." Canadian Mathematical Bulletin 54, no. 2 (2011): 255–69. http://dx.doi.org/10.4153/cmb-2011-011-5.

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AbstractA classical question for a Toeplitz matrix with given symbol is how to compute asymptotics for the determinants of its reductions to finite rank. One can also consider how those asymptotics are affected when shifting an initial set of rows and columns (or, equivalently, asymptotics of their minors). Bump and Diaconis obtained a formula for such shifts involving Laguerre polynomials and sums over symmetric groups. They also showed how the Heine identity extends for such minors, which makes this question relevant to Random Matrix Theory. Independently, Tracy and Widom used the Wiener–Hop

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11

Charlier, Christophe, and Antoine Doeraene. "The generating function for the Bessel point process and a system of coupled Painlevé V equations." Random Matrices: Theory and Applications 08, no. 03 (2019): 1950008. http://dx.doi.org/10.1142/s2010326319500084.

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We study the joint probability generating function for [Formula: see text] occupancy numbers on disjoint intervals in the Bessel point process. This generating function can be expressed as a Fredholm determinant. We obtain an expression for it in terms of a system of coupled Painlevé V equations, which are derived from a Lax pair of a Riemann–Hilbert problem. This generalizes a result of Tracy and Widom [C. A. Tracy and H. Widom, Level spacing distributions and the Bessel kernel, Commun. Math. Phys. 161(2) (1994) 289–309], which corresponds to the case [Formula: see text]. We also provide some

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12

BOROT, GAËTAN, and CÉLINE NADAL. "RIGHT TAIL ASYMPTOTIC EXPANSION OF TRACY–WIDOM BETA LAWS." Random Matrices: Theory and Applications 01, no. 03 (2012): 1250006. http://dx.doi.org/10.1142/s2010326312500062.

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Using loop equations, we compute the large deviation function of the maximum eigenvalue to the right of the spectrum in the Gaussian β matrix ensembles, to all orders in 1/N. We then give a physical derivation of the all order asymptotic expansion of the right tail of Tracy–Widom β laws, for all β > 0, by studying the double scaling limit.

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13

Ferrari, Patrik L., and Herbert Spohn. "A determinantal formula for the GOE Tracy–Widom distribution." Journal of Physics A: Mathematical and General 38, no. 33 (2005): L557—L561. http://dx.doi.org/10.1088/0305-4470/38/33/l02.

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14

Sodin, Sasha. "The Tracy–Widom Law for Some Sparse Random Matrices." Journal of Statistical Physics 136, no. 5 (2009): 834–41. http://dx.doi.org/10.1007/s10955-009-9813-2.

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15

Akemann, Gernot, and Max R. Atkin. "Order analogues of Tracy–Widom distributions via the Lax method." Journal of Physics A: Mathematical and Theoretical 46, no. 1 (2012): 015202. http://dx.doi.org/10.1088/1751-8113/46/1/015202.

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16

Dumaz, Laure, and Bálint Virág. "The right tail exponent of the Tracy–Widom $\beta$ distribution." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 49, no. 4 (2013): 915–33. http://dx.doi.org/10.1214/11-aihp475.

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17

Lee, Ji Oon, and Kevin Schnelli. "Local law and Tracy–Widom limit for sparse random matrices." Probability Theory and Related Fields 171, no. 1-2 (2017): 543–616. http://dx.doi.org/10.1007/s00440-017-0787-8.

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18

Hwang, Jong Yun, Ji Oon Lee, and Wooseok Yang. "Local law and Tracy–Widom limit for sparse stochastic block models." Bernoulli 26, no. 3 (2020): 2400–2435. http://dx.doi.org/10.3150/20-bej1201.

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19

Saccenti, Edoardo, Age K. Smilde, Johan A. Westerhuis, and Margriet M. W. B. Hendriks. "Tracy-Widom statistic for the largest eigenvalue of autoscaled real matrices." Journal of Chemometrics 25, no. 12 (2011): 644–52. http://dx.doi.org/10.1002/cem.1411.

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20

Hwang, Jong Yun, Ji Oon Lee, and Kevin Schnelli. "Local law and Tracy–Widom limit for sparse sample covariance matrices." Annals of Applied Probability 29, no. 5 (2019): 3006–36. http://dx.doi.org/10.1214/19-aap1472.

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21

Sodin, Sasha. "Erratum to: The Tracy–Widom Law for Some Sparse Random Matrices." Journal of Statistical Physics 166, no. 5 (2017): 1343. http://dx.doi.org/10.1007/s10955-017-1715-0.

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22

Bothner, Thomas, and Robert Buckingham. "Large Deformations of the Tracy–Widom Distribution I: Non-oscillatory Asymptotics." Communications in Mathematical Physics 359, no. 1 (2017): 223–63. http://dx.doi.org/10.1007/s00220-017-3006-7.

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23

Witte, N. S., P. J. Forrester, and Christopher M. Cosgrove. "Integrability, random matrices and Painlevé transcendents." ANZIAM Journal 44, no. 1 (2002): 41–50. http://dx.doi.org/10.1017/s1446181100007896.

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AbstractThe probability that an interval I is free of eigenvalues in a matrix ensemble with unitary symmetry is given by a Fredholm determinant. When the weight function in the matrix ensemble is a classical weight function, and the interval I includes an endpoint of the support, Tracy and Widom have given a formalism which gives coupled differential equations for the required probability and some auxiliary quantities. We summarize and extend earlier work by expressing the probability and some of the auxiliary quantities in terms of Painlevé transcendents.

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24

BERTOLA, M., and M. CAFASSO. "THE GAP PROBABILITIES OF THE TACNODE, PEARCEY AND AIRY POINT PROCESSES, THEIR MUTUAL RELATIONSHIP AND EVALUATION." Random Matrices: Theory and Applications 02, no. 02 (2013): 1350003. http://dx.doi.org/10.1142/s2010326313500032.

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We express the gap probabilities of the tacnode process as the ratio of two Fredholm determinants; the denominator is the standard Tracy–Widom distribution, while the numerator is the Fredholm determinant of a very explicit kernel constructed with Airy functions and exponentials. The formula allows us to apply the theory of numerical evaluation of Fredholm determinants and thus produce numerical results for the gap probabilities. In particular we investigate numerically how, in different regimes, the Pearcey process degenerates to the Airy one, and the tacnode degenerates to the Pearcey and Ai

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25

Chen, Lei, and Shaochen Wang. "Moderate deviations for extreme eigenvalues of beta-Laguerre ensembles." Random Matrices: Theory and Applications 09, no. 02 (2019): 2050003. http://dx.doi.org/10.1142/s2010326320500033.

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Let [Formula: see text] be respectively the largest and smallest eigenvalues of beta-Laguerre ensembles with parameters [Formula: see text]. For fixed [Formula: see text], under the condition that [Formula: see text] is much larger than [Formula: see text], we obtain the full moderate deviation principles for [Formula: see text] and [Formula: see text] by using the asymptotic expansion technique. Interestingly, under this regime, our results show that asymptotically the exponential tails of the extreme eigenvalues are Gaussian-type distribution tail rather than the Tracy–Widom-type distributio

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26

Deo, Rohit S. "On the Tracy–Widom approximation of studentized extreme eigenvalues of Wishart matrices." Journal of Multivariate Analysis 147 (May 2016): 265–72. http://dx.doi.org/10.1016/j.jmva.2016.01.010.

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27

Han, Xiao, Guangming Pan, and Bo Zhang. "The Tracy–Widom law for the largest eigenvalue of F type matrices." Annals of Statistics 44, no. 4 (2016): 1564–92. http://dx.doi.org/10.1214/15-aos1427.

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28

Rumanov, Igor. "Painlevé Representation of Tracy–Widom $${_\beta}$$ β Distribution for $${\beta}$$ β = 6". Communications in Mathematical Physics 342, № 3 (2015): 843–68. http://dx.doi.org/10.1007/s00220-015-2487-5.

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29

Onatski, Alexei. "The Tracy–Widom limit for the largest eigenvalues of singular complex Wishart matrices." Annals of Applied Probability 18, no. 2 (2008): 470–90. http://dx.doi.org/10.1214/07-aap454.

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30

Dotsenko, V. "Bethe ansatz derivation of the Tracy-Widom distribution for one-dimensional directed polymers." EPL (Europhysics Letters) 90, no. 2 (2010): 20003. http://dx.doi.org/10.1209/0295-5075/90/20003.

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31

Krishnan, Arjun, and Jeremy Quastel. "Tracy–Widom fluctuations for perturbations of the log-gamma polymer in intermediate disorder." Annals of Applied Probability 28, no. 6 (2018): 3736–64. http://dx.doi.org/10.1214/18-aap1404.

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32

Lee, Ji Oon, and Kevin Schnelli. "Edge universality for deformed Wigner matrices." Reviews in Mathematical Physics 27, no. 08 (2015): 1550018. http://dx.doi.org/10.1142/s0129055x1550018x.

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We consider N × N random matrices of the form H = W + V where W is a real symmetric Wigner matrix and V a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the rescaled distribution of the extremal eigenvalues is given by the Tracy–Widom distribution F1 in the limit of large N. Our proofs also apply to the complex Hermitian setting, i.e. when W is a complex Hermitian

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33

Ma, Zongming. "Accuracy of the Tracy–Widom limits for the extreme eigenvalues in white Wishart matrices." Bernoulli 18, no. 1 (2012): 322–59. http://dx.doi.org/10.3150/10-bej334.

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34

Narayanan, Rajendran, and Martin T. Wells. "On the maximal domain of attraction of Tracy–Widom distribution for Gaussian unitary ensembles." Statistics & Probability Letters 83, no. 10 (2013): 2364–71. http://dx.doi.org/10.1016/j.spl.2013.06.029.

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35

Johnstone, Iain M. "Multivariate analysis and Jacobi ensembles: Largest eigenvalue, Tracy–Widom limits and rates of convergence." Annals of Statistics 36, no. 6 (2008): 2638–716. http://dx.doi.org/10.1214/08-aos605.

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36

Liao, Shiwen, Lu Wei, Taehyung Kim, and Wencong Su. "Modeling and Analysis of Residential Electricity Consumption Statistics: A Tracy-Widom Mixture Density Approximation." IEEE Access 8 (2020): 163558–67. http://dx.doi.org/10.1109/access.2020.3019807.

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37

Johnstone, Iain M., and Zongming Ma. "Fast approach to the Tracy–Widom law at the edge of GOE and GUE." Annals of Applied Probability 22, no. 5 (2012): 1962–88. http://dx.doi.org/10.1214/11-aap819.

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38

Hajiyev, Ch. "Tracy–Widom distribution based fault detection approach: Application to aircraft sensor/actuator fault detection." ISA Transactions 51, no. 1 (2012): 189–97. http://dx.doi.org/10.1016/j.isatra.2011.07.008.

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39

Baik, Jinho, Robert Buckingham, and Jeffery DiFranco. "Asymptotics of Tracy-Widom Distributions and the Total Integral of a Painlevé II Function." Communications in Mathematical Physics 280, no. 2 (2008): 463–97. http://dx.doi.org/10.1007/s00220-008-0433-5.

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40

Lee, Ji Oon, and Kevin Schnelli. "Tracy–Widom distribution for the largest eigenvalue of real sample covariance matrices with general population." Annals of Applied Probability 26, no. 6 (2016): 3786–839. http://dx.doi.org/10.1214/16-aap1193.

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41

Huang, Jiaoyang, Benjamin Landon, and Horng-Tzer Yau. "Transition from Tracy–Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős–Rényi graphs." Annals of Probability 48, no. 2 (2020): 916–62. http://dx.doi.org/10.1214/19-aop1378.

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42

Xu, Shuai-Xia, and Dan Dai. "Tracy–Widom Distributions in Critical Unitary Random Matrix Ensembles and the Coupled Painlevé II System." Communications in Mathematical Physics 365, no. 2 (2018): 515–67. http://dx.doi.org/10.1007/s00220-018-3257-y.

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43

S. Preetham, C., Ch Mahesh, Ch Saranga Haripriya, Ramaraju Anirudh, and M. S. Sireesha. "Spectrum Sensing in Cognitive Radio by Use of Volume-Based Method." International Journal of Engineering & Technology 7, no. 2.17 (2018): 34. http://dx.doi.org/10.14419/ijet.v7i2.17.11554.

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Spectrum sensing is the mission of finding the licensed user signal situation, i.e. to determine the existence and deficiency of primary (licensed) user signal, the recent publications random matrix theory algorithms performs better-quality in spectrum sensing. The RMT fundamental nature is to make use of the distributed extremal eigenvalues of the arrived signal sample covariance matrix (SMC), specifically, Tracy-Widom (TW) distribution which is useful to certain extent in spectrum sensing but demanding for numerical evaluations because there is absence of closed-form expression in it. The sa

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44

El Karoui, Noureddine. "Tracy–Widom limit for the largest eigenvalue of a large class of complex sample covariance matrices." Annals of Probability 35, no. 2 (2007): 663–714. http://dx.doi.org/10.1214/009117906000000917.

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45

Dandekar, Rahul. "A novel recurrence-transience transition and Tracy-Widom growth in a cellular automaton with quenched noise." EPL (Europhysics Letters) 124, no. 2 (2018): 20006. http://dx.doi.org/10.1209/0295-5075/124/20006.

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46

Arifin, Ajib Setyo, and Tomoaki Ohtsuki. "Ergodic Capacity Analysis of Full-duplex Mimo Relay Channel using Tracy-Widom Distribution with Processing Delay." International Journal of Technology 6, no. 2 (2015): 151. http://dx.doi.org/10.14716/ijtech.v6i2.1003.

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47

Chételat, Didier, Rajendran Narayanan, and Martin T. Wells. "On the domain of attraction of a Tracy–Widom law with applications to testing multiple largest roots." Journal of Multivariate Analysis 165 (May 2018): 132–42. http://dx.doi.org/10.1016/j.jmva.2017.11.008.

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48

Dotsenko, Victor. "Bethe ansatz replica derivation of the GOE Tracy–Widom distribution in one-dimensional directed polymers with free endpoints." Journal of Statistical Mechanics: Theory and Experiment 2012, no. 11 (2012): P11014. http://dx.doi.org/10.1088/1742-5468/2012/11/p11014.

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49

Rumanov, Igor. "The correspondence between Tracy–Widom and Adler–Shiota–van Moerbeke approaches in random matrix theory: The Gaussian case." Journal of Mathematical Physics 49, no. 4 (2008): 043503. http://dx.doi.org/10.1063/1.2890428.

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50

Nadal, Celine, and Satya N. Majumdar. "A simple derivation of the Tracy–Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 04 (2011): P04001. http://dx.doi.org/10.1088/1742-5468/2011/04/p04001.

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