Characterization of cutoff for reversible Markov chains
type: Item
instance of: scholarly article
title: Characterization of cutoff for reversible Markov chains
zbMATH Open document ID: 1374.60129
DOI: 10.1214/16-AOP1090
author: Riddhipratim Basu
author: Jonathan Hermon
author: Yuval Peres
published in: The Annals of Probability
publication date: 2017-07-28T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 6754777
zbMATH Keywords: cutoff
zbMATH Keywords: mixing-time
zbMATH Keywords: finite reversible Markov chains
zbMATH Keywords: hitting times
zbMATH Keywords: trees
zbMATH Keywords: maximal inequality
reviewed by: Oleg K. Zakusilo
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6754777