Quenched CLT for random toral automorphism

By Arvind Ayyer, C. Liverani, Mikko Stenlund. 2007

60 citations recorded by the source corpus.

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.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b40219d23c162bff76c2d2ecdd1c823d4247aaa7

Citations in the corpus

• A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems (2017, unknown): “This spectral approach has beenwidely used to prove limit theorems for deterministic dynamics, including large deviation principles [28,44], central limit theorems [6,11,28,45], Berry-Esseen theorems [23,26], local central limit theorems [23,28,45], and vectorvalued almost-sure invariance principles”