Localization of a vertex reinforced random walk on with sub-linear weight

• 成果类型: Article
• 署名作者: Basdevant, Anne-Laure; Schapira, Bruno; Singh, Arvind
• 署名单位: Universite Paris Saclay; Universite Paris Saclay
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0502-3
• 发表日期: 2014
• 页码: 75-115
• 关键词: phase-transition

摘要

We consider a vertex reinforced random walk on the integer lattice with sub-linear reinforcement. Under some assumptions on the regular variation of the weight function, we characterize whether the walk gets stuck on a finite interval. When this happens, we estimate the size of the localization set. In particular, we show that, for any odd number larger than or equal to , there exists a vertex reinforced random walk which localizes with positive probability on exactly consecutive sites.