6533b86ffe1ef96bd12cd511
RESEARCH PRODUCT
Almost sure rates of mixing for i.i.d. unimodal maps
Michael BenedicksVéronique Maume-deschampsViviane Baladisubject
Independent and identically distributed random variables[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]Mathematics::Dynamical SystemsMarkov chainGeneral Mathematics010102 general mathematicsMathematical analysisErgodicityAbsolute continuity01 natural sciencesExponential function[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]010104 statistics & probabilityQuadratic equationInvariant measure0101 mathematicsExponential decayddc:510Mathematicsdescription
International audience; 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, and Baladi and 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 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, and on the other a probabilistic coupling method introduced by Young to study rates of mixing, we prove stretched exponential upper bounds for the almost sure rates of mixing.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-01-01 |