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Asymptotics for random intermittent maps

Banff International Research Station for Mathematical Innovation and Discovery

This talk reports on joint work with Wael Bahsoun and Yuejiao Duan, University of Lough- borough, UK.\r\nExpanding interval maps with a neutral fixed point are some of the simplest examples of nonuniformly hyperbolic systems. They are frequently studied for their potential to give in- teresting statistical behaviour such as sub-exponential decay of correlation, intermittency or so-called anomalous di↵usion (di↵erent terms that amount to essentially the same thing: slow relaxation to equilibrium).\r\nA random map (skew product with a Bernoulli shift) constructed from a family of such nonuniformly hyperbolic maps undoubtedly inherits some of these intermittency features, but exactly how they combine may not be immediately obvious. We will show, for example, that the rate of correlation decay is completely determined by the ‘least nonuniformly hyperbolic’ map in the family, no matter how infrequently the map is chosen in the randomization. Once you guess the result, the reason behind this principle is actually rather transparent and amounts to an elementary calculation about large deviations in Bernoulli trials.

Mathematics; Dynamical systems and ergodic theory; Probability theory and stochastic processes; Dynamical systems

video/mp4

Author affiliation: University of Victoria

2015-07-25

Attribution-NonCommercial-NoDerivs 2.5 Canada

http://hdl.handle.net/2429/54162

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/2.5/ca/