SPECTRAL THEORY FOR WEAKLY REVERSIBLE MARKOV CHAINS

Autor(en): Wuebker, Achim
Stichwörter: BOUNDS; CONVERGENCE; general state space; INEQUALITIES; isoperimetric constant; Markov chain; Mathematics; reversibility; spectral gap property; Statistics & Probability
Erscheinungsdatum: 2012
Herausgeber: CAMBRIDGE UNIV PRESS
Journal: JOURNAL OF APPLIED PROBABILITY
Volumen: 49
Ausgabe: 1
Startseite: 245
Seitenende: 265
Zusammenfassung: 
The theory of L-2-spectral gaps for reversible Markov chains has been studied by many authors. In this paper we consider positive recurrent general state space Markov chains with stationary transition probabilities. Replacing the assumption of reversibility with a weaker assumption, we still obtain a simple necessary and sufficient condition for the spectral gap property of the associated Markov operator in terms of the isoperimetric constant. We show that this result can be applied to a large class of Markov chains, including those that are related to positive recurrent finite-range random walks on Z.
ISSN: 00219002

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