Functional central limit theorems for vicious walkers 

作成者 香取, 眞理, 種村, 秀紀
作成者の別表記 Katori, Makoto, Tanemura, Hideki
日本十進分類法 (NDC) 421.5
内容 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,∞) 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.
コンテンツの種類 プレプリント Preprint
DCMI資源タイプ text
ファイル形式 application/x-dvi
DOI 10.1080/10451120310001633711
掲載誌情報 Stochastics and stochastics reports Vol.75 no.6 page.369-390 (2003)
言語 英語
関連情報 (hasVersion)
著者版フラグ author

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