LOCALIZATION ON 4 SITES FOR VERTEX-REINFORCED RANDOM WALKS ON Z
成果类型：
Article
署名作者：
Basdevant, Anne-Laure; Schapira, Bruno; Singh, Arvind
署名单位：
Universite Paris Nanterre; Universite Paris Saclay; Universite Paris Saclay
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/12-AOP811
发表日期：
2014
页码：
527-558
关键词：
摘要：
We characterize nondecreasing weight functions for which the associated one-dimensional vertex reinforced random walk (VRRW) localizes on 4 sites. A phase transition appears for weights of order n log log n: for weights growing faster than this rate, the VRRW localizes almost surely on, at most, 4 sites, whereas for weights growing slower, the VRRW cannot localize on less than 5 sites. When w is of order n log log n, the VRRW localizes almost surely on either 4 or 5 sites, both events happening with positive probability.