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Title: Mixing rates and limit theorems for random intermittent maps
Authors: Bahsoun, Wael
Bose, Christopher
Keywords: Interval maps with a neutral fixed point
Random dynamical systems
Limit laws
Decay of correlations
Stable laws
Issue Date: 2016
Publisher: © IOP Publishing Ltd & London Mathematical Society
Citation: BAHSOUN, W. and BOSE, C., 2016. Mixing rates and limit theorems for random intermittent maps. Nonlinearity, 29 (4), pp. 1417 - 1433.
Abstract: We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps T using the full parameter range 0< < , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0< <1) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1 < we study a second class of random transformations derived from piecewise affine Gaspard–Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.
Description: This is an author-created, un-copyedited version of an article published in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0951-7715/29/4/1417.
Sponsor: The second author is supported by a research grant from the National Sciences and Engineering Research Council of Canada.
Version: Accepted for publication
DOI: 10.1088/0951-7715/29/4/1417
URI: https://dspace.lboro.ac.uk/2134/21030
Publisher Link: http://dx.doi.org/10.1088/0951-7715/29/4/1417
ISSN: 0951-7715
Appears in Collections:Published Articles (Maths)

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