Measure concentration through non-Lipschitz observables and functional   inequalities
  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 covers diffusions as well as pure-jump Markov processes on unbounded spaces. 
Arnaud Guillin, Ald\'eric Joulin (IMT)
math.PR