Mixing time is the amount of time it takes for a Markov chain to get sufficiently close to its stationary distribution, where the probabilities of being in different states stabilize. Understanding mixing time is crucial because it provides insight into how quickly a Markov chain converges, which impacts various applications, such as random walks and algorithms in statistical physics. A smaller mixing time indicates a faster convergence, which is often desirable in practical scenarios like sampling or optimization problems.
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