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

Article Article scientifique Article Almost sure rates of mixing for i.i.d. unimodal maps eng 2002 author Baladi Viviane 23031 author Benedicks Michael author Maume-Deschamps Véronique 126545 77-126 10.1016/s0012-9593(01)01083-7 0012-9593 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. Dewey 510 25 Section de mathématiques 11 false Annales scientifiques de l'École normale supérieure 35 1 c3e99b90-d66e-47d0-b96a-bc3d80e6934e Article (Published version) Public ASENS_2002_4_35_1_77_0.pdf 546160 application/pdf openAccess Faculté des sciences / Section de mathématiques

Title	Published in	Year	Views	Downloads

Almost sure rates of mixing for i.i.d. unimodal maps	Annales scientifiques de l'École normale supérieure	2002	688	836
Projective metrics and mixing properties on towers	Transactions of the American Mathematical Society	2001	546	337

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