random_intermittent2015_final.pdf (343.68 kB)
Download file

Mixing rates and limit theorems for random intermittent maps

Download (343.68 kB)
journal contribution
posted on 22.04.2016, 10:43 by Wael BahsounWael Bahsoun, Christopher Bose
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.

Funding

The second author is supported by a research grant from the National Sciences and Engineering Research Council of Canada.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Nonlinearity

Volume

29

Issue

4

Pages

1417 - 1433

Citation

BAHSOUN, W. and BOSE, C., 2016. Mixing rates and limit theorems for random intermittent maps. Nonlinearity, 29 (4), pp. 1417 - 1433.

Publisher

© IOP Publishing Ltd & London Mathematical Society

Version

AM (Accepted Manuscript)

Publication date

2016

Notes

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.

ISSN

0951-7715

eISSN

1361-6544

Language

en