Random matrix central limit theorems for nonintersecting random walks
Authors:
- Jinho BaikJBJinho Baik
- Toufic M. SuidanTSToufic M. Suidan
Open Access
- 1 September 2007
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 35 (5) , 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.Keywords
All Related Versions
This publication has 44 references indexed in Scilit:
- Universality at the edge of the spectrum for unitary, orthogonal, and symplectic ensembles of random matricesCommunications on Pure and Applied Mathematics, 2006
- A remark on a theorem of Chatterjee and last passage percolationJournal of Physics A: General Physics, 2006
- A model for the bus system in Cuernavaca (Mexico)Journal of Physics A: General Physics, 2006
- PDEs for the joint distributions of the Dyson, Airy and Sine processesThe Annals of Probability, 2005
- Non-intersecting paths, random tilings and random matricesProbability Theory and Related Fields, 2002
- Random walks and random permutationsJournal of Physics A: General Physics, 2001
- Semiclassical Asymptotics of Orthogonal Polynomials, Riemann-Hilbert Problem, and Universality in the Matrix ModelAnnals of Mathematics, 1999
- Matrices coupled in a chain: I. Eigenvalue correlationsJournal of Physics A: General Physics, 1998
- Coincident probabilities and applications in combinatoricsJournal of Applied Probability, 1988
- Coincidence probabilitiesPacific Journal of Mathematics, 1959