Functional central limit theorems for vicious walkers
| dc.creator | Katori, Makoto | |
| dc.creator | Tanemura, Hideki | |
| dc.date | 2002-03-28 | |
| dc.date | 2004-02-25 | |
| dc.date.accessioned | 2026-07-07T04:47:19Z | |
| dc.date.available | 2026-07-07T04:47:19Z | |
| dc.description | 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 $(0,T]$ for the first type and in an infinite time interval $(0,\infty)$ 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. | |
| dc.description | AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for publication | |
| dc.identifier | https://arxiv.org/abs/math/0203286 | |
| dc.identifier | http://arxiv.org/abs/math/0203286 | |
| dc.identifier | Stoch. Stoch. Rep. 75 (2003) 369-390 | |
| dc.identifier | doi:10.1080/10451120310001633711 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63671 | |
| dc.subject | Probability | |
| dc.subject | Combinatorics | |
| dc.title | Functional central limit theorems for vicious walkers | |
| dc.type | text |