PHASE TRANSITION FOR THE ONCE-REINFORCED RANDOM WALK ON Zd-LIKE TREES

• 成果类型: Article
• 署名作者: Kious, Daniel; Sidoravicius, Vladas
• 署名单位: New York University; New York University; NYU Shanghai
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1222
• 发表日期: 2018
• 页码: 2121-2133
• 关键词: random environment; recurrence

摘要

In this short paper, we consider the Once-reinforced random walk with reinforcement parameter a on trees with bounded degree which are transient for the simple random walk. On each of these trees, we prove that there exists an explicit critical parameter a(0) such that the Once-reinforced random walk is almost surely recurrent if a > a(0) and almost surely transient if a < a(0). This provides the first examples of phase transition for the Once-reinforced random walk.