RECURRENCE AND TRANSIENCE OF MULTIDIMENSIONAL ELEPHANT RANDOM WALKS

• 成果类型: Article
• 署名作者: Qin, Shuo
• 署名单位: New York University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1728
• 发表日期: 2025
• 页码: 1049-1078
• 关键词: branching-processes; urn schemes

摘要

We prove a conjecture by Bertoin that the multidimensional elephant random walk on Zd is transient in dimensions d >= 3. We show that it undergoes a phase transition in dimensions d = 1, 2 between recurrence and transience at p = (2d + 1)/(4d).