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We give a bound on the mixing time of a uniformly ergodic, reversible Markovchain in terms of the spectral radius of the transition operator. This boundhas been established previously in finite state spaces, and is widely believedto hold in general state spaces, but a proof has not been provided to ourknowledge.

A Lower Bound on the Mixing Time of Uniformly Ergodic Markov Chains in Terms of the Spectral Radius