Events & Seminars

2018 Jan 02

Dynamics Lunch: Ohad Feldheim (HUJI) "Finitely dependent proper colouring of Z"

12:00pm to 1:00pm

An M-dependent process X(n) on the integers, is a process for which every event concerning with X(-1),X(-2),... is independent from every event concerning with X(M),X(M+1),... Such processes play an important role both as scaling limits of physical systems and as a tool in approximating other processes. A question that has risen independently in several contexts is: "is there an M dependent proper colouring of the integer lattice for some finite M?"
2017 Dec 05

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

12:00pm to 1:00pm

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.