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.
Publié le : 2007-09-14
Classification:
Nonintersecting random walks,
Tracy–Widom distribution,
sine kernel,
strong approximation,
Riemann–Hilbert problem,
Stieltjes–Wigert polynomials,
60F05
@article{1189000929,
author = {Baik, Jinho and Suidan, Toufic M.},
title = {Random matrix central limit theorems for nonintersecting random walks},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 1807-1834},
language = {en},
url = {http://dml.mathdoc.fr/item/1189000929}
}
Baik, Jinho; Suidan, Toufic M. Random matrix central limit theorems for nonintersecting random walks. Ann. Probab., Tome 35 (2007) no. 1, pp. 1807-1834. http://gdmltest.u-ga.fr/item/1189000929/