University of Birmingham > Talks@bham > Topology and Dynamics Seminar > Quenched decay of correlations for slowly mixing systems

Quenched decay of correlations for slowly mixing systems

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We study random towers that are suitable to analyse the statistics of slowly mixing random systems. We obtain upper bounds on the rate of 'quenched' correlation decay in a general setting.  We apply our results to the random family of Liverani-Saussol-Vaienti maps with parameters in $[\alpha_0,\alpha_1]\subset (0,1)$ chosen independently with respect to a distribution $\nu$ on $[\alpha_0,\alpha_1]$ and show that the quenched decay of correlation is governed by the fastest mixing map in the family.  
In particular, we prove that for every $\delta >0$, for almost every $\omega \in [\alpha_0,\alpha_1]^\mathbb{Z}$, the upper bound $n^{1-\frac{1}{\alpha_0}+\delta}$ holds on the rate of decay of correlation for Hölder observables on the fibre over $\omega$. 
This is a joint work with W. Bahsoun and C. Bose.

This talk is part of the Topology and Dynamics Seminar series.

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