Quenched decay of correlations for slowly mixing systems

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• Dr. Marks Ruziboev (Loughborough University)
• Thursday 14 March 2019, 13:00-14:00
• Lecture Room C, Department of Mathematics.

If you have a question about this talk, please contact Tony Samuel.

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.

This talk is included in these lists:

• Lecture Room C, Department of Mathematics
• School of Mathematics events
• Topology and Dynamics seminar

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