标题： Glauber动力学快速混合的熵独立性方法应用于单调系统 显示英文标题

标题： Rapid Mixing of Glauber Dynamics for Monotone Systems via Entropic Independence

摘要： 我们研究单调系统上的Glauber动力学的混合时间。 对于满足熵独立性条件的单调系统，我们证明了Glauber动力学的新混合时间比较结果。 对于具体应用，我们得到了由铁磁Ising模型在一致偏置外部场下诱导的随机簇模型的$\tilde{O}(n)$混合时间，以及在单边唯一性条件下双射硬球模型的$\tilde{O}(n^2)$混合时间，其中$n$是相应模型中的变量数量，分别改进了[Chen和Zhang, SODA'23]和[Chen, Liu和Yin, FOCS'23]中的最佳已知结果。 我们的证明结合了经典屏蔽不等式中随机支配论证的思想和最近发展的高维扩展器的想法。 证明的关键步骤是针对单调系统，Glauber动力学与场动力学之间的新颖比较结果。 显示英文摘要

摘要： We study the mixing time of Glauber dynamics on monotone systems. For monotone systems satisfying the entropic independence condition, we prove a new mixing time comparison result for Glauber dynamics. For concrete applications, we obtain $\tilde{O}(n)$ mixing time for the random cluster model induced by the ferromagnetic Ising model with consistently biased external fields, and $\tilde{O}(n^2)$ mixing time for the bipartite hardcore model under the one-sided uniqueness condition, where $n$ is the number of variables in corresponding models, improving the best known results in [Chen and Zhang, SODA'23] and [Chen, Liu, and Yin, FOCS'23], respectively. Our proof combines ideas from the stochastic dominance argument in the classical censoring inequality and the recently developed high-dimensional expanders. The key step in the proof is a novel comparison result between the Glauber dynamics and the field dynamics for monotone systems.