The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer from observations. In this paper, we advocate for the use of the average-mixing time as a more optimistic and demonstrably easier-to-estimate alternative. We further illustrate its applicability across a range of settings, from two-point to countable spaces, and discuss some practical implications.

翻译：马尔可夫链收敛至平稳分布的速度通常通过总变差混合时间这一概念进行评估。然而，这一最坏情形度量往往得出悲观估计，并且难以从观测中推断。本文提倡使用平均混合时间作为一种更为乐观且明显更易于估计的替代方案。我们进一步阐释了其在从两点空间到可数空间等一系列场景中的适用性，并探讨了一些实际意义。