The Annals of Probability

Random matrix central limit theorems for nonintersecting random walks

Jinho Baik and Toufic M. Suidan

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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.

Article information

Source
Ann. Probab., Volume 35, Number 5 (2007), 1807-1834.

Dates
First available in Project Euclid: 5 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1189000929

Digital Object Identifier
doi:10.1214/009117906000001105

Mathematical Reviews number (MathSciNet)
MR2349576

Zentralblatt MATH identifier
1131.60015

Subjects
Primary: 60F05: Central limit and other weak theorems

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

Citation

Baik, Jinho; Suidan, Toufic M. Random matrix central limit theorems for nonintersecting random walks. Ann. Probab. 35 (2007), no. 5, 1807--1834. doi:10.1214/009117906000001105. https://projecteuclid.org/euclid.aop/1189000929


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