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Mixing times are hitting times of large sets

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We consider irreducible reversible discrete time Markov chains on a finite state space. Mixing times and hitting times are fundamental parameters of the chain. In this talk, we relate them by showing that the mixing time of the lazy chain is equivalent to the maximum over initial states x and large sets A of the hitting time of A starting from x. As an application, we show that the mixing time on a finite binary tree is robust to bounded change of edge conductances. (Joint work with Yuval Peres)

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