半图、其他非稳定度序列和切换马尔可夫链
Half-graphs, other non-stable degree sequences, and the switch Markov chain
摘要：
使用开关的蒙特卡罗马尔可夫链方法提供了生成具有给定度序列的随机图的最简单方法之一。开关马尔可夫链收敛于均匀分布，但一般不知道收敛的收敛速率。通过对各种度序列的研究，建立了所谓的$P$ -稳定度序列（包括有向图的度序列）的快速混合，它覆盖了度序列的所有已知的快速混合区域.本文给出了一类非平凡的度序列，它们不是$P$ -稳定的，而开关马尔可夫链在它们上面仍然是快速混合的。这个族与Tyshkevich分解和强稳定性有着密切的联系。
英文摘要：
One of the simplest methods of generating a random graph with a given degree sequence is provided by the Monte Carlo Markov Chain method using switches. The switch Markov chain converges to the uniform distribution, but generally the rate of convergence is not known. After a number of results concerning various degree sequences, rapid mixing was established for so-called $P$-stable degree sequences (including that of directed graphs), which covers every previously known rapidly mixing region of degree sequences. In this paper we give a non-trivial family of degree sequences that are not $P$-stable and the switch Markov chain is still rapidly mixing on them. This family has an intimate connection to Tyshkevich-decompositions and strong stability as well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
