Estimate Mixing Time Of The Finite Markov Chain

Finite Markov chain plays an important role in the computer algorithm.In the Markov chain Monte Carlo algorithm.The mixing time is an important concept. On the one hand, the size of the available mixing time is the quality criterion of the randomized algorithm; On the other hand, when analyzing the error of algorithm, the mixing time is also an important basis. This paper introduces some specific Markov chains, especially the mixing time and Stationary time. And for some specific Markov chain, giving the estimate of the mixing time (ie, the upper bound estimate of the mixing time and lower bound estimate).