动态Erdens-Rényi图上随机游动的截断
Cutoff for Random Walk on Dynamical Erdős--Rényi Graph
摘要：
我们考虑完全图$K_n$上的动态渗流，其中每个边以速率$μ\ll 1/n$刷新其状态，然后以概率$p = λ/n$声明开放，其中$λ> 1$。我们研究了一个随机游动在这个动态环境中跳跃率$1/n$沿每个开放的边缘。我们证明了全系统的混合时间在$\log n/μ$处具有截止。我们通过证明随机游动成分的混合速度快于环境过程来做到这一点;在此过程中，我们控制了游动变得孤立所需的时间。
英文摘要：
We consider dynamical percolation on the complete graph $K_n$, where each edge refreshes its state at rate $μ\ll 1/n$, and is then declared open with probability $p = λ/n$ where $λ> 1$. We study a random walk on this dynamical environment which jumps at rate $1/n$ along every open edge. We show that the mixing time of the full system exhibits cutoff at $\log n/μ$. We do this by showing that the random walk component mixes faster than the environment process; along the way, we control the time it takes for the walk to become isolated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
