Global observables for random walks: law of large numbers

Dmitry Dolgopyat, Marco Lenci, Péter Nándori

We consider the sums $T_N={\sum }_{n=1}^{N}F(S_n)$ where $S_n$ is a random walk on ${\mathbb{Z}}^d$ and $F:{\mathbb{Z}}^d\to \mathbb{R}$ is a global observable, that is, a bounded function wh…