2002/03/31 by Makoto Katori, Hideki Tanemura
Mathematics · #Advanced Combinatorial Mathematics #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.CO #math.PR
paper · pdf · doi:10.1080/10451120310001633711
published as Stoch. Stoch. Rep. 75 (2003) 369-390 · AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for publication
openalex publication_date 2003/12/01 · arxiv created 2004/02/25 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We consider the diffusion scaling limit of the vicious walker model that is a system of nonintersecting random walks. We prove a functional central limit theorem for the model and derive two types of nonintersecting Brownian motions, in which the nonintersecting condition is imposed in a finite time interval for the first type and in an infinite time interval for the second type, respectively. The limit process of the first type is a temporally inhomogeneous diffusion, and that of the second type is a temporally homogeneous diffusion that is identified with a Dyson's model of Brownian motions studied in the random matrix theory. We show that these two types of processes are related to each other by a multi-dimensional generalization of Imhof's relation, whose original form relates the Brownian meander and the three-dimensional Bessel process. We also study the vicious walkers with wall restriction and prove a functional central limit theorem in the diffusion scaling limit.