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Measure concentration through non-Lipschitz observables and functional inequalities. (English) Zbl 1282.60024

Summary: 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.

MSC:

60E15 Inequalities; stochastic orderings
60J27 Continuous-time Markov processes on discrete state spaces
60J60 Diffusion processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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