Flat trace statistics of the transfer operator of a random partially expanding map

Abstract

We consider the skew-product of an expanding map E on the circle with an almost surely random perturbation τ = τ0 + δτ of a deterministic function τ0:. The associated transfer operator can be decomposed with respect to frequency in the y variable into a family of operators acting on functions on the circle:. We show that the flat traces of behave as normal distributions in the semi classical limit n, ξ → ∞ up to the Ehrenfest time n ⩽ ck log ξ.