A Combinatorial Approach to a Model of Constrained Random Walkers

被引：2

作者：

Espinasse, T. ^{[1
]}

Guillotin-Plantard, N. ^{[1
]}

Nadeau, P. ^{[1
]}

机构：

[1] Univ Lyon 1, CNRS UMR 5208, Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

来源：

COMBINATORICS PROBABILITY & COMPUTING | 2016年 / 25卷 / 02期

关键词：

Functional analysis;

D O I：

10.1017/S096354831500005X

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In [1], the authors consider a random walk (Z(n), (1), ... ,Z(n,K+ 1)) is an element of Z(K+1) with the constraint that each coordinate of the walk is at distance one from the following coordinate. A functional central limit theorem for the first coordinate is proved and the limit variance is explicited. In this paper, we study an extended version of this model by conditioning the extremal coordinates to be at some fixed distance at every time. We prove a functional central limit theorem for this random walk. Using combinatorial tools, we give a precise formula of the variance and compare it with that obtained in [1].

引用

页码：222 / 235

页数：14