Fluctuation of ergodic averages and other stochastic processes

Sovanlal Mondal, Joe Rosenblatt, Máté Wierdl

For an ergodic map $T$ and a non-constant, real-valued $f\in L^1$, the ergodic averages ${\mathbb{A}}_{N}f(x)=\frac{1}{N}{\sum }_{n=1}^{N}f(T^{n}x)$ converge a.e., but the convergence…