Title: Temporal distributional limit theorems for dynamical systems
Speaker: Omri Sarig
Speaker Info: Weizmann Institute
Brief Description:
Special Note:
Abstract:
Suppose T:X-->X is a dynamical system, f:X-->R is a "nice" function, and x is a FIXED initial condition. The sequence of ergodic sums at x, S(n,x)=f(x)+f(Tx)+...+f(T^n x), is often very oscillatory. In such cases it makes sense to look for scaling limits for the distribution of values of S(n,x), n=1,...,N as N tends to infinity. Such results are called "temporal distributional limit theorems" and they reveal interesting, sometimes surprising, information. We will discuss the examples of irrational rotations, horocycle flows, and Anosov diffeomorphisms. (Joint work with D. Dolgopyat).Date: Tuesday, February 21, 2017