Quenched decay of correlations for slowly mixing systems

Wael Bahsoun
Loughborough University

Date(s) : 19/09/2017   iCal
11 h 00 min - 12 h 00 min

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 [α0, α1] ⊂ (0,1), with 0 < α0 < 1/2, chosen independently with respect to a distribution ν on [α0, α1] and show that the quenched decay of correlation is governed by the fastest mixing map in the family. In particular, for three different distributions ν on [α0, α1] (discrete, uniform, quadratic), we derive sharp asymptotics on the measure of return-time intervals for the quenched dynamics, ranging from {n}-1/α0 to (log {n}) · {n}-1/α0 and to (log {n})2 · {n}-1/α0 respectively.




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