Number of times a site is visited in two-dimensional random walks

In this paper, formulas are derived to compute the mean number of times a site has been visited in a random walk on a two-dimensional lattice. Asymmetric random walks are considered, with or without drift, for different boundary conditions. It is shown that in case of absorbing boundaries the mean number of visits reaches stationary values over the lattice; comparisons with a Monte Carlo simulation are also presented.