Abstract
We study a large class of reversible Markov chains with discrete state space and transition matrix PN. We define the notion of a set of metastable points as a subset of the state space ΓN such that (i) this set is reached from any point x∈ΓN without return to x with probability at least bN, while (ii) for any two points x, y in the metastable set, the probability T− 1x,y to reach y from x without return to x is smaller than aN− 1< bN. Under some additional non-degeneracy assumption, we show that in such a situation:
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