Quenched decay of correlations for slowly mixing systems
Wael Bahsoun
Loughborough University
https://www.lboro.ac.uk/departments/maths/staff/academic/wael-bahsoun/
Date(s) : 19/09/2017 iCal
11h00 - 12h00
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.
https://arxiv.org/abs/1706.04158
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