Mixing and decorrelation in infinite measure: the case of the periodic sinai billiard

Françoise Pène (1, 2, 3)

1 LM - Laboratoire de mathématiques de Brest
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
3 UBO - Université de Brest

We investigate the question of the rate of mixing for observables of a Z d-extension of a probability preserving dynamical system with good spectral properties. We state general mixing results, including expansions of every order. The main part of this article is devoted to the study of mixing rate for smooth observables of the Z 2-periodic Sinai billiard, with different kinds of results depending on whether the horizon is finite or infinite. We establish a first order mixing result when the horizon is infinite. In the finite horizon case, we establish an asymptotic expansion of every order, enabling the study of the mixing rate even for observables with null integrals.

Mots clés: Sinai billiard; Lorentz process; Young tower; local limit theorem; decorrelation; mixing; infinite measure

Domaines: Systèmes dynamiques [math.DS]

Françoise Pène. Mixing and decorrelation in infinite measure: the case of the periodic sinai billiard. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2019, 55 (1), ⟨10.1214/18-AIHP885⟩. ⟨hal-01538631⟩