Viviane Baladi, Michael Benedicks, Veronique Maume-Deschamps
Almost sure rates of mixing for i.i.d. unimodal maps
(643K, Postscript)
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.