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November 2010 Curvature, concentration and error estimates for Markov chain Monte Carlo
Aldéric Joulin, Yann Ollivier
Ann. Probab. 38(6): 2418-2442 (November 2010). DOI: 10.1214/10-AOP541


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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Aldéric Joulin. Yann Ollivier. "Curvature, concentration and error estimates for Markov chain Monte Carlo." Ann. Probab. 38 (6) 2418 - 2442, November 2010.


Published: November 2010
First available in Project Euclid: 24 September 2010

zbMATH: 1207.65006
MathSciNet: MR2683634
Digital Object Identifier: 10.1214/10-AOP541

Primary: 60J22 , 62E17 , 65C05

Keywords: concentration of measure , Markov chain Monte Carlo , Ricci curvature , Wasserstein distance

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 6 • November 2010
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