Quenched CLT for random toral automorphism

Details Quenched CLT for random toral automorphism Quenched CLT for random toral automorphism

2007-11-24

arxiv.org/abs/0711.3818v1

Discrete and Continuous Dynamical Systems - A, Volume 24, Issue 2, 2009, pp. 331-348

Mathematics

Dynamical Systems

18 pages

Scientific paper

10.3934/dcds.2009.24.331

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.

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