随机环境中的分支随机游走
Branching random walk in random environment
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中文总结 AI 辅助
研究随机环境（伯努利位点渗流）下d维分支随机游走，在不同子代分布假设下分析条件生存概率，两种子代分布临界时建立Yaglom定理。
中文摘要 AI 辅助
我们考虑d维整数格点Z^d上的分支随机游走，其随机环境由参数p∈(0,1)的伯努利位点渗流给出。该模型中，位于开放位点的每个粒子按分布μ_∘繁殖，位于闭合位点的粒子按另一分布μ_•繁殖；每个新生子粒子从父代位置出发执行独立的简单随机游走跳跃。我们在(μ_∘, μ_•)的不同假设下研究条件生存概率，并在两种子代分布均为临界时建立Yaglom定理。
英文摘要
We consider a branching random walk on \(\Z^d\) in a random environment given by Bernoulli site percolation with parameter \(p\in (0,1)\). In this model, each particle located at an open site reproduces according to a law \(μ_\circ\), whereas a particle at a closed site reproduces according to another law \(μ_\bullet\). Each newly born child performs an independent simple random walk jump from the position of its parent. We study the quenched survival probability under various assumptions on \((μ_\circ, μ_\bullet)\) and establish a Yaglom theorem when both offspring distributions are critical.
