Strong law of large numbers for a function of the local times of a transient random walk in ${\mathbb{Z}}^d$

I. M. Asymont, D. Korshunov

For an arbitrary transient random walk $(S_n{)}_{n\ge 0}$ in ${\mathbb{Z}}^d$, $d\ge 1$, we prove a strong law of large numbers for the spatial sum ${\sum }_{x\in {\mathbb{Z}}^d}f(l(n,x))$ of…