Once reinforced random walk on Z x Γ

被引：1

作者：

Kious, Daniel ^{[1
]}

Schapira, Bruno ^{[2
]}

Singh, Arvind ^{[3
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Aix Marseille Univ, I2M, Cent Marseille, CNRS,UMR 7373, F-13453 Marseille, France

[3] Univ Paris Sud, Lab Math, F-91405 Orsay, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2021年 / 57卷 / 04期

关键词：

Recurrence; Reinforced random walk; Self-interacting random walk; Shape theorem; JUMP PROCESS;

D O I：

10.1214/21-AIHP1151

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We revisit Vervoort's unpublished paper (Vervoort (2002)) on the once reinforced random walk, and prove that this process is recurrent on any graph of the form Z x Gamma, with F a finite graph, for sufficiently large reinforcement parameter. We also obtain a shape theorem for the set of visited sites, and show that the fluctuations around this shape are of polynomial order. The proof involves sharp general estimates on the time spent on subgraphs of the ambiant graph which might be of independent interest.

引用

页码：2219 / 2242

页数：24