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

Electronic Communications in Probability

Jiro Akahori¹ 

关键词: self-interacting random walks;    reinforced random walks;   

DOI  :  10.1214/19-ECP240

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

We study the behaviour of a class of edge-reinforced random walks on $\mathbb{Z} _{+}$, 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].

【 授权许可】

CC BY