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Quenched decay of correlations for slowly mixing systems

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journal contribution
posted on 15.11.2019 by Wael Bahsoun, Christopher Bose, Marks Ruziboev
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 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 Society

Volume

372

Issue

9

Pages

6547-6587

Citation

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 Society

Version

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

18/01/2019

Publication date

2019-05-23

Copyright date

2019

ISSN

0002-9947

eISSN

1088-6850

Language

en

Exports

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