Scientific article
Open access

Almost sure rates of mixing for i.i.d. unimodal maps

Published inAnnales scientifiques de l'École normale supérieure, vol. 35, no. 1, p. 77-126
Publication date2002

It has been known since the pioneering work of Jakobson and subsequent work by Benedicks and 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 and Young [8], and Baladi and Viana [4] 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 stationary measures of i.i.d. itineraries are more difficult to estimate than the “averaged statistics”. Adapting to random systems, on the one hand partitions associated to hyperbolic times due to Alves [1], and on the other a probabilistic coupling method introduced by Young [26] to study rates of mixing, we prove stretched exponential upper bounds for the almost sure rates of mixing.

Citation (ISO format)
BALADI, Viviane, BENEDICKS, Michael, MAUME-DESCHAMPS, Véronique. Almost sure rates of mixing for i.i.d. unimodal maps. In: Annales scientifiques de l’École normale supérieure, 2002, vol. 35, n° 1, p. 77–126. doi: 10.1016/s0012-9593(01)01083-7
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Article (Published version)
ISSN of the journal0012-9593

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