The mixing time for simple exclusion
The mixing time for simple exclusion
复制标题
简单排除的混合时间
DOI：
--
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
B. Morris
中科院分区：
文献类型：
--
作者：
B. Morris
我们得到了$\mathbf{Z}^d/L\mathbf {Z}^d$中含有$k\leq{1/2}L^d$粒子的排斥过程的混合时间的紧界为O（L^2\log k）$.以前的最佳界限，根据日志索伯列夫常数确定的丘，是不紧的小$k$。当依赖于维度$d$被认为是，我们的界限是一个改进的所有$k$。我们还得到了比以前估计更低阶的弛豫时间的界：我们的界为O（L^2\log d）$，改进了Quastel得到的早期界为O（L^2d）$。我们的证明是基于一个辅助马尔可夫链，我们称之为变色龙过程，这可能是独立的利益。
We obtain a tight bound of $O(L^2\log k)$ for the mixing time of the exclusion process in $\mathbf{Z}^d/L\mathbf{Z}^d$ with $k\leq{1/2}L^d$ particles. Previously the best bound, based on the log Sobolev constant determined by Yau, was not tight for small $k$. When dependence on the dimension $d$ is considered, our bounds are an improvement for all $k$. We also get bounds for the relaxation time that are lower order in $d$ than previous estimates: our bound of $O(L^2\log d)$ improves on the earlier bound $O(L^2d)$ obtained by Quastel. Our proof is based on an auxiliary Markov chain we call the chameleon process, which may be of independent interest.