Decay of random correlation functions for unimodal maps

Since the pioneering results of Jakobson and subsequent work by Benedicks-C arleson and others, it is known that quadratic maps f(a) (x) = a - x(2) adm it a unique absolutely continuous invariant measure for a positive measure set of parameters a. For topologically mixing f(a), Young and Keller-Nowick i independently proved exponential decay of correlation functions for this a.c.i.m. and smooth observables. We consider random compositions of small p erturbations f + omega (t), with f = f(a) or another unimodal map satisfyin g certain nonuniform hyperbolicity axioms, and omega (t) chosen independent ly and identically in [-epsilon, epsilon]. Baladi-Viana showed exponential mixing of the associated Markov chain, i.e., averaging over all random itin eraries. We obtain stretched exponential bounds for the random correlation functions of Lipschitz observables for the sample measure mu (omega), of al most every itinerary.