Monday 22 Oct 2018: Dynamics Seminar: Quenched decay of correlations for slowly mixing systems
Wael Bahsoun - Loughborough
We introduce 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 general 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 a ‘generic' 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.