Fredrickson-Andersen单自旋易化模型
Fredrickson-Andersen one spin facilitated model out of equilibrium
摘要：
本文研究了多项式增长的无限连通图上的Fredrickson和Andersen单自旋促进模型（FA 1f）。速率为1的每个站点分别以概率$p\in[0,1]$或$q=1-p$将其占用变量刷新为填充或空状态，前提是其最近的邻居中至少有一个是空的。我们研究了从不同于平稳乘积$p$ -Bernoulli测度$μ$的初始分布$ν$出发的非平衡动力学.我们假设，在$ν$下，两个最近的空站点之间的平均距离是一致有界的。然后，我们证明当空位密度$q$高于适当阈值$\bar q<1$时收敛到平衡。收敛是指数或拉伸指数，这取决于图的增长。特别地，对于$d=1$，它在$\bbZ^d$上是指数的，而对于$d>1$，它是拉伸指数的。我们的结果可以推广到其他非合作模型。
英文摘要：
We consider the Fredrickson and Andersen one spin facilitated model (FA1f) on an infinite connected graph with polynomial growth. Each site with rate one refreshes its occupation variable to a filled or to an empty state with probability $p\in[0,1]$ or $q=1-p$ respectively, provided that at least one of its nearest neighbours is empty. We study the non-equilibrium dynamics started from an initial distribution $ν$ different from the stationary product $p$-Bernoulli measure $μ$. We assume that, under $ν$, the mean distance between two nearest empty sites is uniformly bounded. We then prove convergence to equilibrium when the vacancy density $q$ is above a proper threshold $\bar q<1$. The convergence is exponential or stretched exponential, depending on the growth of the graph. In particular it is exponential on $\bbZ^d$ for $d=1$ and stretched exponential for $d>1$. Our result can be generalized to other non cooperative models.
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