Characterization of cutoff for reversible Markov chains (Q2012242)

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.