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Quenched decay of correlations for slowly mixing systems
Version 2 2019-11-15, 10:48
Version 1 2019-01-18, 10:29
journal contribution
posted on 2019-11-15, 10:48 authored by Wael BahsounWael Bahsoun, Christopher Bose, Marks RuziboevWe 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 LiveraniSaussol-Vaienti maps with parameters in [α0, α1] ⊂ (0, 1) 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, we prove that for
every δ > 0, for almost every ω ∈ [α0, α1]
Z, the upper bound n
1− 1
α0
+δ
holds on
the rate of decay of correlation for Holder observables on the fibre over ¨ ω. For three
different distributions ν on [α0, α1] (discrete, uniform, quadratic), we also derive sharp
asymptotics on the measure of return-time intervals for the quenched dynamics, ranging
from n
− 1
α0 to (log n)
1
α0 · n
− 1
α0 to (log n)
2
α0 · n
− 1
α0 respectively.
Funding
WB and MR would like to thank The Leverhulme Trust for supporting their research through the research grant RPG-2015-346. CB’s research is supported by a research grant from the National Sciences and Engineering Research Council of Canada.
History
School
- Science
Department
- Mathematical Sciences
Published in
Transactions of the American Mathematical SocietyVolume
372Issue
9Pages
6547-6587Citation
BAHSOUN, W., BOSE, C. and RUZIBOEV, M.B., 2019. Quenched decay of correlations for slowly mixing systems. Transactions of the American Mathematical Society, 372(9), pp. 6547-6587.Publisher
© American Mathematical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
First published in Transactions of the American Mathematical Society, in 372(9), pp. 6547-6587, published by the American Mathematical Society,Acceptance date
2019-01-18Publication date
2019-05-23Copyright date
2019ISSN
0002-9947eISSN
1088-6850Publisher version
Language
- en