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Mixing rates and limit theorems for random intermittent maps
journal contribution
posted on 2016-04-22, 10:43 authored by Wael BahsounWael Bahsoun, Christopher BoseWe 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
NonlinearityVolume
29Issue
4Pages
1417 - 1433Citation
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 SocietyVersion
- AM (Accepted Manuscript)
Publication date
2016Notes
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
0951-7715eISSN
1361-6544Publisher version
Language
- en