AI 中文总结
研究d维环面上动态渗流中最近邻Glauber动力学的混合时间，证明当p<p_c(d)且λ足够小时，混合时间阶为log N/λ。
AI 中文摘要
我们研究了对应于动态渗流上最近邻Glauber动力学的随机自旋系统的混合时间，定义在边长为$N$的$d$维环面上。在该模型中，每条边的状态（开放或关闭）以速率$\lambda>0$独立更新，根据$\mathrm{Ber}(p)$样本。同时，每个位点的自旋以速率$1$根据限制在开放边上的环境上的Glauber动力学更新。我们证明，对于相对一般的最近邻系统类，只要$p<p_c(d)$，对于任何温度，如果$\lambda$足够小，混合时间阶为$\frac{\log N}{\lambda}$。该马尔可夫链是不可逆的，证明通过开发一种特定的耦合来实现，该耦合在环境表现良好时耦合局部配置。
英文摘要
We study the mixing times of stochastic spin systems corresponding to nearest-neighbour Glauber dynamics on dynamical percolation, defined on $d$-dimensional torus of side-length $N$. In this model, the status of each edge (open or closed) updates independently at rate $λ>0$, according to $\mathrm{Ber}(p)$ samples. Simultaneously, the spin of each site updates at rate $1$ according to Glauber dynamics on the environment restricted to open edges. We show that for a relatively general class of nearest-neighbour systems, as long as $p<p_c(d)$, for any temperature, if $λ$ is sufficiently small, the mixing time is of order $\frac{\log N}λ$. This Markov chain is non-reversible, and the proof is obtained by developing a particular coupling that couples together local configurations whenever the environment behaves well.
CommentsImproved presentation of the main results
