Random matrix central limit theorems for nonintersecting random walks

• 成果类型: Article
• 署名作者: Baik, Jinho; Suidan, Toufic M.
• 署名单位: University of Michigan System; University of Michigan; University of California System; University of California Santa Cruz
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000001105
• 发表日期: 2007
• 页码: 1807-1834
• 关键词: orthogonal polynomials; uniform asymptotics; UNIVERSALITY; airy; distributions; ensembles; Respect; EQUATIONS; weights; SYSTEM

摘要

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.