LOW-DIMENSIONAL LONELY BRANCHING RANDOM WALKS DIE OUT

• 成果类型: Article
• 署名作者: Birkner, Matthias; Sun, Rongfeng
• 署名单位: Johannes Gutenberg University of Mainz; National University of Singapore
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1271
• 发表日期: 2019
• 页码: 774-803
• 关键词: systems; persistence; criteria; particle; Markov

摘要

The lonely branching random walks on Z(d) is an interacting particle system where each particle moves as an independent random walk and undergoes critical binary branching when it is alone. We show that if the symmetrized walk is recurrent, lonely branching random walks die out locally. Further-more, the same result holds if additional branching is allowed when the walk is not alone.