Sovan Mondal
The Ohio State University
Title
Fluctuation of ergodic averages and other stochastic processes
Abstract
For an ergodic map T and a non-constant, real-valued L1 function f, the ergodic averages converge for almost every x, but the convergence is never monotone. Depending on particular properties of the function f , the averages may or may not actually fluctuate around the mean value infinitely often almost everywhere. One of the main results that we will discuss in this talk is that almost everywhere fluctuation around the mean is the generic behavior. That is, for a fixed ergodic T , the generic L1 function f has the property that the averages fluctuating around the mean infinitely often for almost every x. We will also talk about fluctuation for other stochastic processes, namely the ergodic averages along a subsequence, convolution operators and martingales.
This is a joint work with Joseph Rosentblatt and Máté Wierdl.
