Joulin, Aldéric; Guillin, Arnaud Measure concentration through non-Lipschitz observables and functional inequalities. (English) Zbl 1282.60024 Electron. J. Probab. 18, Paper No. 65, 26 p. (2013). 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. Cited in 2 Documents 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 Keywords:concentration; invariant measure; reversible Markov process; Lyapunov condition; functional inequality; carré du champ; diffusion process; jump process PDFBibTeX XMLCite \textit{A. Joulin} and \textit{A. Guillin}, Electron. J. Probab. 18, Paper No. 65, 26 p. (2013; Zbl 1282.60024) Full Text: DOI arXiv