Moments and distribution of the local time of a two-dimensional random walk

Let l (n, x) be the local time of a random walk on Z(2). We prove a strong law of large numbers for the quantity L-n (alpha) = Sigma(x is an element of Z2) l(n, x)(alpha) for all alpha >= 0. We use this result to describe the distribution of the local time of a typical point in the range of the random walk. (C) 2006 Elsevier B.V. All rights reserved.