# COMPARISON THEOREMS FOR REVERSIBLE MARKOV CHAINS

```@article{Diaconis1993COMPARISONTF,
title={COMPARISON THEOREMS FOR REVERSIBLE MARKOV CHAINS},
author={Persi Diaconis and Laurent Saloff-Coste},
journal={Annals of Applied Probability},
year={1993},
volume={3},
pages={696-730}
}```
• Published 1 August 1993
• Mathematics
• Annals of Applied Probability
By symmetry, P has eigenvalues 1 = I03 > I381 > ?> I 31xI- 1 2 -1. This paper develops methods for getting upper and lower bounds on 8i3 by comparison with a second reversible chain on the same state space. This extends the ideas introduced in Diaconis and Saloff-Coste (1993), where random walks on finite groups were considered. The bounds involve geometric properties such as the diameter and covering number of an associated graph along the lines of Diaconis and Stroock (1991). The main…
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