Mixing time and expansion of non-negatively curved Markov chains

Florentin Münch, J. Salez
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引用次数: 4

Abstract

We establish three remarkable consequences of non-negative curvature for sparse Markov chains. First, their conductance decreases logarithmically with the number of states. Second, their displacement is at least diffusive until the mixing time. Third, they never exhibit the cutoff phenomenon. The first result provides a nearly sharp quantitative answer to a classical question of Ollivier, Milman and Naor. The second settles a conjecture of Lee and Peres for graphs with non-negative curvature. The third offers a striking counterpoint to the recently established cutoff for non-negatively curved chains with uniform expansion.
非负弯曲马尔可夫链的混合时间与展开
我们建立了稀疏马尔可夫链非负曲率的三个显著结果。首先,它们的电导随状态数呈对数递减。其次,它们的位移至少在混合时间之前是弥漫性的。第三,他们从不表现出切断现象。第一个结果为Ollivier, Milman和Naor的经典问题提供了一个近乎尖锐的定量答案。第二部分解决了Lee和Peres关于非负曲率图的一个猜想。第三种方法与最近建立的具有均匀膨胀的非负弯曲链的截止提供了惊人的对位。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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