On Mixing Properties of Reversible Markov Chains

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.

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