Electronic Journal of Probability

Measure concentration through non-Lipschitz observables and functional inequalities

Aldéric Joulin and Arnaud Guillin

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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.

Article information

Electron. J. Probab., Volume 18 (2013), paper no. 65, 26 pp.

Accepted: 24 June 2013
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 60E15: Inequalities; stochastic orderings 60J27: Continuous-time Markov processes on discrete state spaces 60J60: Diffusion processes [See also 58J65] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Concentration invariant measure reversible Markov process Lyapunov condition functional inequality diffusion process jump process

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Joulin, Aldéric; Guillin, Arnaud. Measure concentration through non-Lipschitz observables and functional inequalities. Electron. J. Probab. 18 (2013), paper no. 65, 26 pp. doi:10.1214/EJP.v18-2425. https://projecteuclid.org/euclid.ejp/1465064290

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