Quenched central limit theorem for random walks with a spectral gap

Jean-Pierre Conze (1) , Stéphane Le Borgne (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Let G be a semi-group of measure preserving transformations of a probability space (X, B, m) and let mu be a probability measure on G. We prove a quenched central limit theorem for functions in L(0)(p)(m), p > 2, when the spectral gap condition holds for the diagonal action of G on (X x X, m circle times m). (C) 2011 Academie des sciences.

Mots clés: CLT

Domaines: Probabilités [math.PR]; Systèmes dynamiques [math.DS]

Jean-Pierre Conze, Stéphane Le Borgne. Quenched central limit theorem for random walks with a spectral gap. Comptes Rendus. Mathématique, 2011, 349 (13-14), pp.801-805. ⟨10.1016/j.crma.2011.06.017⟩. ⟨hal-00675930⟩