Global observables for RW: Law of large numbers
Global observables for RW: Law of large numbers
We consider the sums TN=∑n=1NF(Sn) where Sn is a random walk on Zd and F:Zd→R is a global observable, that is, a bounded function which admits an average value when averaged over large cubes. We show that TN always satisfies the weak Law of Large Numbers but the strong law …