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Download fileMixing rates and limit theorems for random intermittent maps
journal contribution
posted on 22.04.2016, 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