Central limit theorem for stationary products of toral automorphisms

Jean-Pierre Conze (1) , Stéphane Le Borgne (1) , Mikaël Roger (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Chercheur indépendant

Let (A(n)(omega)) be a stationary process in M-d*(Z). For a Holder function f on T-d we consider the sums Sigma(n)(k=1) f((t)A(k)(omega) (t)A(k-1)(omega) ... tA(1)(omega) x mod 1) and prove a Central Limit Theorem for a.e. omega in different situations in particular for "kicked" stationary processes. We use the method of multiplicative systems of Komlos and the Multiplicative Ergodic Theorem.

Mots clés: Toral automorphisms; central limit theorem; multiplicative system; kicked stationary process; Lyapunov exponents

Domaines: Probabilités [math.PR]

Jean-Pierre Conze, Stéphane Le Borgne, Mikaël Roger. Central limit theorem for stationary products of toral automorphisms. Discrete and Continuous Dynamical Systems - Series S, 2012, 32 (5), pp.1597-1626. ⟨10.3934/dcds.2012.32.1597⟩. ⟨hal-00681695⟩