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.
"Measure concentration through non-Lipschitz observables and functional inequalities." Electron. J. Probab. 18 1 - 26, 2013. https://doi.org/10.1214/EJP.v18-2425