Measure concentration through non-Lipschitz observables and functional inequalities

Aldéric Joulin (Université de Toulouse)
Arnaud Guillin (Université de Clermont-Ferrand)

Abstract


Non-Gaussian concentration estimates are obtained for invariant probability measures of reversible Markov processes. We show that the functional inequalities approach combined with a suitable Lyapunov condition allows us to circumvent the classical Lipschitz assumption of the observables. Our method is general and offers an unified treatment of diffusions and pure-jump Markov processes on unbounded spaces.

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Pages: 1-26

Publication Date: June 24, 2013

DOI: 10.1214/EJP.v18-2425

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