Random matrix central limit theorems for nonintersecting random walks
Jinho Baik and Toufic M. Suidan
Source: Ann. Probab. Volume 35, Number 5 (2007), 1807-1834.
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.
Primary Subjects: 60F05
Keywords: Nonintersecting random walks; Tracy–Widom distribution; sine kernel; strong approximation; Riemann–Hilbert problem; Stieltjes–Wigert polynomials
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1189000929
Digital Object Identifier: doi:10.1214/009117906000001105
Mathematical Reviews number (MathSciNet):
MR2349576
Zentralblatt MATH identifier:
1131.60015
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