Transitions for exceptional times in dynamical first-passage percolation

• 成果类型: Article
• 署名作者: Damron, Michael; Hanson, Jack; Harper, David; Lam, Wai-Kit
• 署名单位: University System of Georgia; Georgia Institute of Technology; City University of New York (CUNY) System; City College of New York (CUNY); National Taiwan University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01178-1
• 发表日期: 2023
• 页码: 1039-1085
• 关键词: invasion percolation; LIMIT-THEOREMS; exponents; BEHAVIOR

摘要

In first-passage percolation (FPP), we let(tau(v))be i.i.d. nonnegative weights on thevertices of a graph and study the weight of the minimal path between distant vertices. If Fi s the distribution function of tau v, there are different regimes: if F(0) is small,this weight typically grows like a linear function of the distance, and when F(0) islarge, the weight is typically of order one. In between these is the critical regime inwhich the weight can diverge, but does so sublinearly. We study a dynamical version ofcritical FPP on the triangular lattice where vertices resample their weights according toindependent rate-one Poisson processes. We prove that if n-expressionry sumexpressiontion (F-1)(1/2+1/2(k))=infinity,then a.s. there are exceptional times at which the weight grows atypically, but if n-expressionry sumexpressiontion k(7/8)F(-1)(1/2+1/2(k))