Measure concentration through non-Lipschitz observables and functional inequalities

Arnaud Guillin (1) , Aldéric Joulin (2)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: Concentration; invariant measure; reversible Markov process; Lyapunov condition; functional inequality; carré du champ; diffusion process; jump process

Domaines: Probabilités [math.PR]; Analyse fonctionnelle [math.FA]

Arnaud Guillin, Aldéric Joulin. Measure concentration through non-Lipschitz observables and functional inequalities. Electronic Journal of Probability, 2013, 18. ⟨hal-00668800⟩