Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained, bipartite, and directed sequences, using different mechanisms.

The aim of this paper is to unify these approaches. We will illustrate the strength of the unified method by showing that on any $P$-stable family of unconstrained/bipartite/directed degree sequences the switch Markov chain is rapidly mixing. This is a common generalization of every known result that shows the rapid mixing nature of the switch Markov chain on a region of degree sequences. Among the applications of this general result is an almost uniform sampler for power-law and heavy-tailed degree sequences. Another application shows that the switch Markov chain on the degree sequence of an Erdős-Rényi random graph $G(n,p)$ is asymptotically almost surely rapidly mixing if $p$ is bounded away from 0 and 1 by at least $\frac{5logn}{n-1}$.

自 1997 年以来，人们花费了大量精力来研究切换马尔可夫链在简单图的图度序列的实现上的混合时间。使用不同机制在无约束、二分和有向序列上快速混合马尔可夫链的几个结果得到了证明。

本文的目的是统一这些方法。我们将通过展示在任何$磷$-稳定的无约束/二分/有向度序列家族，转换马尔可夫链正在快速混合。这是每个已知结果的普遍推广，显示了转换马尔可夫链在度数序列区域上的快速混合性质。这个一般结果的应用之一是几乎统一的幂律和重尾度序列采样器。另一个应用表明，Erdős-Rényi 随机图的度数序列上的开关马尔可夫链$G(n,磷)$ 渐近地几乎肯定会快速混合，如果 $磷$ 距离 0 和 1 的界限至少为 $\frac{5日志n}{n-1}$.