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By P. H. Peskun. Biometrika 60(3), 607–612.

Original scan: www2.stat.duke.edu/~scs/Courses/Stat376/Papers/ConvergeRates/Peskun1973.pdf

Primary publisher metadata and original scan identify the transition comparison for Monte Carlo chains with a common stationary distribution. The wiki states a finite-state reversible form and supplies its own Dirichlet-form and inverse-operator explanation. The scan's text layer contains only its cover; no unverified precise equation locator is claimed.

P. H. Peskun authored the 1973 paper underlying Peskun ordering, a comparison of the efficiency of Markov chain Monte Carlo algorithms with the same stationary target.^[ref]

For finite reversible Markov chains, increasing every off-diagonal transition probability while preserving the stationary law cannot increase the asymptotic variance of time averages. The comparison formalizes why spending less time repeating the current state can help statistical estimation, provided the ordering's hypotheses hold. It compares the variance of estimators, not merely their one-step acceptance rates.^[ref]