期刊
ANNALS OF PROBABILITY
卷 38, 期 6, 页码 2418-2442出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/10-AOP541
关键词
Markov chain Monte Carlo; concentration of measure; Ricci curvature; Wasserstein distance
We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a positive curvature assumption expressing a kind of metric ergodicity, which generalizes the Ricci curvature from differential geometry and, on finite graphs, amounts to contraction under path coupling.
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