Abstract: Consider the contact process on homogeneous trees in a random environment, in which the recovery rates {δ(x): x∈T_d} are i.i.d. random variables (bounded above) while the infection rate is a constant λ. The contact process survives locally for every λ>0 if {lim inf }[v→∞] e^βvP(logδ(x)>v)>0 for all β>0.

Key words: contact process, random environment, local survival

摘要： 考虑齐次树上随机环境下的接触过程，随机环境是指康复的速率{δ(x): x∈T_d}是独立同分布而且有上界的随机变量，感染的速率是常数λ。如果 lim inf[v→∞]e^βvP(-logδ(x)>v)>0, β>0, 则对任意的λ>0，接触过程是强蔓延的。

关键词: 接触过程, 随机环境, 强蔓延