Reversible Markov chains: variational representations and ordering

Chris Sherlock

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arXiv · 1809.01903

Reversible Markov chains: variational representations and ordering

Chris Sherlock

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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.

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Chris Sherlock. 2025-06-19. Reversible Markov chains: variational representations and ordering. https://arxiv.org/abs/1809.01903

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