DECAY OF RANDOM CORRELATION FUNCTIONS FOR UNIMODAL MAPS

Since the pioneering results of Jakobson and subsequent work by ABenedicks- Carleson and others, it is known that quadratic maps fa(x) A= a-x^2 admit a unique absolutely continuous invariant measure for a Apositive measure set of parameters a. For topologically mixing fa, AYoung and Keller-Nowicki independently proved exponential decay of Acorrelation functions for this a.c.i.m. and smooth observables. We consider random compositions of small perturbations f +we)t, with / A= fa or another unimodal map satisfying certain nonuniform Ahyperbolicity axioms, and u>t chosen independently and identically in A[- e,e]. Baladi-Viana showed exponential mixing of the associated AMarkov chain, i.e., averaging over all random itineraries. We obtain stretched exponential bounds for the random correlation Afunctions of Lipschitz observables for the sample measure flu, of Aalmost every itinerary.