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Almost sure rates of mixing for i.i.d. unimodal maps
KTH, Superseded Departments, Mathematics.
2002 (English)In: Annales Scientifiques de l'Ecole Normale Supérieure, ISSN 0012-9593, Vol. 35, no 1, 77-126 p.Article in journal (Refereed) Published
Abstract [en]

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 proper-ties 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 [I], 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.

Place, publisher, year, edition, pages
2002. Vol. 35, no 1, 77-126 p.
Keyword [en]
lasota-yorke maps, random perturbations, limit-theorems, srb measures, transformations, dynamics, interval, systems
URN: urn:nbn:se:kth:diva-21420ISI: 000174641800003OAI: diva2:340118
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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