Optimal concentration inequalities for dynamical systems

Jean-René Chazottes (1) , Sebastien Gouezel (2)

1 CPHT - Centre de Physique Théorique [Palaiseau]
2 IRMAR - Institut de Recherche Mathématique de Rennes

For dynamical systems modeled by a Young tower with exponential tails, we prove an exponential concentration inequality for all separately Lipschitz observables of n variables. When tails are polynomial, we prove polynomial concentration inequalities. Those inequalities are optimal. We give some applications of such inequalities to specific systems and specific observables.

Domaines: Systèmes dynamiques [math.DS]

Jean-René Chazottes, Sebastien Gouezel. Optimal concentration inequalities for dynamical systems. 2011. ⟨hal-00637855v1⟩