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@article{Blumenthal:2023:10.1214/23-aop1627,
author = {Blumenthal, A and Coti, Zelati M and Gvalani, RS},
doi = {10.1214/23-aop1627},
journal = {The Annals of Probability},
pages = {1559--1601},
title = {Exponential mixing for random dynamical systems and an example of Pierrehumbert},
url = {http://dx.doi.org/10.1214/23-aop1627},
volume = {51},
year = {2023}
}

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TY  - JOUR
AB  - We consider the question of exponential mixing for random dynamical systems on arbitrary compact manifolds without boundary. We put forward a robust, dynamics-based framework that allows us to construct space-time smooth, uniformly bounded in time, universal exponential mixers. The framework is then applied to the problem of proving exponential mixing in a classical example proposed by Pierrehumbert in 1994, consisting of alternating periodic shear flows with randomized phases. This settles a longstanding open problem on proving the existence of a space-time smooth (universal) exponentially mixing incompressible velocity field on a two-dimensional periodic domain while also providing a toolbox for constructing such smooth universal mixers in all dimensions.
AU  - Blumenthal,A
AU  - Coti,Zelati M
AU  - Gvalani,RS
DO  - 10.1214/23-aop1627
EP  - 1601
PY  - 2023///
SN  - 0091-1798
SP  - 1559
TI  - Exponential mixing for random dynamical systems and an example of Pierrehumbert
T2  - The Annals of Probability
UR  - http://dx.doi.org/10.1214/23-aop1627
VL  - 51
ER  -

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