CAPACITY OF THE RANGE OF TREE-INDEXED RANDOM WALK

• 成果类型: Article
• 署名作者: Bai, Tianyi; Wan, Yijun
• 署名单位: New York University; NYU Shanghai; Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1689
• 发表日期: 2022
• 页码: 1557-1589
• 关键词: branching random-walks

摘要

By introducing a new measure for the infinite Galton-Watson process and providing estimates for (discrete) Green's functions on trees, we establish the asymptotic behavior of the capacity of critical branching random walks: in high dimensions d >= 7, the capacity grows linearly; and in the critical dimension d = 6, it grows asymptotically proportional to n/log n.