Dynamics Lunch: Jon Aaronson (TA) "Title: "Classical probability theory" for processes generated by expanding C^2 interval maps via quasicompactness."

Abstract: It was noticed in the 30's by Doeblin & Forte that Markov operators with "chains with complete connections" act quasi-compactly on the Lipschitz functions. These are operators like the transfer operators of certain expanding C^2 interval maps (e.g. the square of Gauss map). It is folklore that stochastic processes generated by smooth observables under these maps satisfy many of the results of "classical probability theory" (e.g. CLT, Chernoff inequality). I'll try to explain some of this in a "lunchtime" mode.


Tue, 05/12/2017 - 12:00 to 13:00