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September 2007 Random matrix central limit theorems for nonintersecting random walks
Jinho Baik, Toufic M. Suidan
Ann. Probab. 35(5): 1807-1834 (September 2007). DOI: 10.1214/009117906000001105

Abstract

We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity, several limiting distributions of the walks at the mid-time behave as the eigenvalues of random Hermitian matrices as the dimension of the matrices grows to infinity.

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Jinho Baik. Toufic M. Suidan. "Random matrix central limit theorems for nonintersecting random walks." Ann. Probab. 35 (5) 1807 - 1834, September 2007. https://doi.org/10.1214/009117906000001105

Information

Published: September 2007
First available in Project Euclid: 5 September 2007

zbMATH: 1131.60015
MathSciNet: MR2349576
Digital Object Identifier: 10.1214/009117906000001105

Subjects:
Primary: 60F05

Keywords: Nonintersecting random walks , Riemann–Hilbert problem , Sine kernel , Stieltjes–Wigert polynomials , strong approximation , Tracy–Widom distribution

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 5 • September 2007
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