Reversible Markov chains: variational representations and ordering
Statistics Theory
2025-06-23 v2 Computation
Statistics Theory
Abstract
This pedagogical document explains three variational representations that are useful when comparing the efficiencies of reversible Markov chains: (i) the Dirichlet form and the associated variational representations of the spectral gaps; (ii) a variational representation of the asymptotic variance of an ergodic average; and (iii) the conductance, and the equivalence of a non-zero conductance to a non-zero right spectral gap.
Cite
@article{arxiv.1809.01903,
title = {Reversible Markov chains: variational representations and ordering},
author = {Chris Sherlock},
journal= {arXiv preprint arXiv:1809.01903},
year = {2025}
}
Comments
Updated references, improved consistency of notation, corrected minor errors