Quenched CLT for random toral automorphism

Abstract

We establish a quenched Central Limit Theorem (CLT) for a smooth observable of random sequences of iterated linear hyperbolic maps on the torus. To this end we also obtain an annealed CLT for the same system. We show that, almost surely, the variance of the quenched system is the same as for the annealed system. Our technique is the study of the transfer operator on an anisotropic Banach space specifically tailored to use the cone condition satisfied by the maps.

18 pages

Cited by in corpus (13)

• Annealed and quenched limit theorems for random expanding dynamical systems
• A spectral approach for quenched limit theorems for random expanding dynamical systems
• Central limit theorems for sequential and random intermittent dynamical systems
• Mixing rates and limit theorems for random intermittent maps
• A central limit theorem for time-dependent dynamical systems
• Decay of correlation for random intermittent maps
• Limit theorems for random expanding or hyperbolic dynamical systems and vector-valued observables
• Recurrence for quenched random Lorentz tubes
• Quenched normal approximation for random sequences of transformations
• Deterministic Walks in Quenched Random Environments of Chaotic Maps
• Multi-Gaussian modes of diffusion in a quenched random medium
• Stability and approximation of statistical limit laws for multidimensional piecewise expanding maps
• Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps