99-460 Viviane Baladi, Michael Benedicks, Veronique Maume-Deschamps

Almost sure rates of mixing for i.i.d. unimodal maps (643K, Postscript) Dec 2, 99

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Abstract. It has been known since the pioneering work of Jakobson and subsequent work by Benedicks-Carleson and others that a positive measure set of quadratic maps admit an absolutely continuous invariant measure. Young and Keller-Nowicki proved exponential decay of its correlation functions. Benedicks-Young and Baladi-Viana studied stability of the density and exponential rate of decay of the Markov chain associated to i.i.d. small perturbations. The almost sure statistical properties of the sample measures of i.i.d. itineraries are more difficult to estimate than the "averaged statistics." Adapting to random systems, on the one hand the notion of hyperbolic times due to Alves and on the other a probabilistic coupling method introduced by Young to study rates of mixing, we prove stretched exponential bounds for the almost sure rates of mixing.

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