论文标题
合并和分支简单的对称排除过程
Coalescing and branching simple symmetric exclusion process
论文作者
论文摘要
由动力学约束的相互作用粒子系统（KCM）的动机，我们考虑了一般有限图上的可逆合并和分支简单的排除过程$ g =（v，e）$ dual dual dual dual dual dual dual to $ g $。我们的主要目标是在其对数Sobolev常数和放松时间上的紧密界限，特别关注精致的略微临界状态，在这种状态下，颗粒的平衡密度倾向于零为$ | v | \ rightArrow \ rightarrow \ infty $。我们的结果使我们能够非常直接地恢复并改善到$ \ ell^p $混合，$ p \ ge 2 $，以及在更多一般图表上，Pillai和Smith的混合时间结果是Fredrickson-Andersen的一个自旋（FA-$ 1 $ F）kcm，在Divceete $ d $ d $ d $ d $ dimemential torus上。鉴于对更复杂的fa- $ j $ f kcm，$ j> 1 $的申请，我们还将部分分析扩展到具有更通用的产品状态空间的类似过程。
Motivated by kinetically constrained interacting particle systems (KCM), we consider a reversible coalescing and branching simple exclusion process on a general finite graph $G=(V,E)$ dual to the biased voter model on $G$. Our main goal are tight bounds on its logarithmic Sobolev constant and relaxation time, with particular focus on the delicate slightly supercritical regime in which the equilibrium density of particles tends to zero as $|V|\rightarrow \infty$. Our results allow us to recover very directly and improve to $\ell^p$-mixing, $p\ge 2$, and to more general graphs, the mixing time results of Pillai and Smith for the Fredrickson-Andersen one spin facilitated (FA-$1$f) KCM on the discrete $d$-dimensional torus. In view of applications to the more complex FA-$j$f KCM, $j>1$, we also extend part of the analysis to an analogous process with a more general product state space.
