Spectral Theory for Weakly Reversible Markov Chains
2012 ◽
Vol 49
(01)
◽
pp. 245-265
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Keyword(s):
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.
2012 ◽
Vol 49
(1)
◽
pp. 245-265
◽
1960 ◽
Vol 40
(12)
◽
pp. 574-574
1985 ◽
Vol 22
(01)
◽
pp. 123-137
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Keyword(s):
1975 ◽
Vol 12
(04)
◽
pp. 744-752
◽
Keyword(s):
1991 ◽
Vol 19
(3)
◽
pp. 907-928
◽