Distribution Functions for Largest Eigenvalues and Their Applications

By Craig A. Tracy, Harold Widom. 2002

143 citations recorded by the source corpus.

It is now believed that the limiting distribution function of the largest eigenvalue in the three classic random matrix models GOE, GUE and GSE describe new universal limit laws for a wide variety of processes arising in mathematical physics and interacting particle systems. These distribution

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/131fcf58090efe6ab2cef94c7789c9c4062f5ec1

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

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Citations in the corpus

A pedestrian's view on interacting particle systems, KPZ universality and random matrices (2008, background): “For further information we refer the reader to the surveys [1, 60, 68, 88, 125, 129] and the monograph [11].”
A Universality Property for Last-Passage Percolation Paths Close to the Axis (2004, unknown): “Hence in particular (e.g. [16]) (cid:2) (cid”
Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matrices (2005, background): “The distributions F (L0), β = 1, 2, 4, are the celebrated Tracy–Widom distributions which turn out to have applications in an extraordinary variety of different areas of pure and applied mathematics (see for example the recent review [TW6]).”
Topics in Random Matrix Theory (2012, result): “the paper [DeGi2007], which (like many of the other references cited above) builds upon the original work of Tracy and Widom [TrWi2002] that handled special ensembles such as GOE and GUE.”
Painlevé formulas of the limiting distributions for nonnull complex sample covariance matrices (2005, background): “As a part of the proof, a representation of orthogonal polynomials on the unit circle in terms of an operator on a discrete set is presented.”
A GUE central limit theorem and universality of directed first andlast passage site percolation (2004, background): “Introduction In the last few years, it has become clear that random matrix theory is intimately related to a variety of questions arising in physics, statistics, combinatorics, representation theory, number theory, and probability theory (see e.g. [12, 5, 10, 19]).”
Poisson–Dirichlet distribution for random Belyi surfaces (2005, background): “Tracy and Widom [53, 54] computed the limiting distribution function for the largest eigenvalue in the classical Gaussian ensembles; these distribution functions are expressed in terms of a certain Painlevé II function and are now believed to describe new universal limit laws for a wide variety of p”
Non-asymptotic theory of random matrices: extreme singular values (2010, background): “The occurrence of Tracy-Widom law in random matrix theory and several other areas was the subject of an ICM 2002 talk of Tracy and Widom [91].”
Spectral Radii of Large Non-Hermitian Random Matrices (2014, background): “, [51] and [29] and the references therein).”