Phase transitions for edge-reinforced random walks on the half-line

被引：2

作者：

Akahori, Jiro ^{[1
]}

Collevecchio, Andrea ^{[2
]}

Takei, Masato ^{[3
]}

机构：

[1] Ritsumeikan Univ, Dept Math Sci, Kyoto, Japan

[2] Monash Univ, Sch Math Sci, Melbourne, Vic, Australia

[3] Yokohama Natl Univ, Fac Engn, Dept Appl Math, Yokohama, Kanagawa, Japan

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2019年 / 24卷

基金：

澳大利亚研究理事会;

关键词：

self-interacting random walks; reinforced random walks;

D O I：

10.1214/19-ECP240

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 study the behaviour of a class of edge-reinforced random walks on Z(+), with heterogeneous initial weights, where each edge weight can be updated only when the edge is traversed from left to right. We provide a description for different behaviours of this process and describe phase transitions that arise as trade-offs between the strength of the reinforcement and that of the initial weights. Our result aims to complete the ones given by Davis [3, 4], Takeshima [9, 10] and Vervoort [11].

引用

页数：12

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