On Mixing Properties of Reversible Markov Chains

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New Zealand Journal of Mathematics

Vol. 45, (2015), Pages 71-87


Richard C. Bradley

Department of Mathematics,

Indiana University,

Bloomington, Indiana 47405,

U.S.A.

mailto:bradleyr@indiana.edu






Abstract It is well known that for a strictly stationary, reversible, Harris recurrent Markov chain, the ρ-mixing condition is equivalent to geometric ergodicity and to a spectral gap condition. In this note, it will be shown with an example that for that class of Markov chains, the interlaced variant of the ρ-mixing condition fails to be equivalent to those conditions.

Keywords reversible Markov chain, ρ-mixing, ρ * -mixing, geometric ergodicity.

Classification (MSC2000) 60G10, 60J05, 60J10.

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