{
  "id": "math/0203286",
  "version": "v6",
  "published": "2002-03-28T03:05:50.000Z",
  "updated": "2004-02-25T04:13:16.000Z",
  "title": "Functional central limit theorems for vicious walkers",
  "authors": [
    "Makoto Katori",
    "Hideki Tanemura"
  ],
  "comment": "AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for publication",
  "journal": "Stoch. Stoch. Rep. 75 (2003) 369-390",
  "doi": "10.1080/10451120310001633711",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2004-02-25T04:13:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional central limit theorem",
      "vicious walker",
      "diffusion scaling limit",
      "brownian motions",
      "first type"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......3286K"
    }
  }
}