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Characterization of cutoff for reversible Markov chains. (English) Zbl 1374.60129
A sequence of Markov chains is said to exhibit (total variation) cutoff if the convergence to stationarity in total variation distance is abrupt. A chain is called lazy if $$P(x,x) \geqslant {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}$$, for all $$x$$. Theorem 1 gives a sharp spectral condition for cutoff in lazy weighted nearest-neighbor random walks on trees. Theorem 2 gives conditions for cutoff to exhibit for a generalization of birth and death chains. Theorem 3 considers sequences of lazy reversible irreducible finite chains.

##### MSC:
 60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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