Random walks on abelian groups
R. M. Dudley · Proceedings of the American Mathematical Society · 1962
By random walk I shall mean a Markov chain with homogeneous transition probabilities p(a, b) =p(O, b-a) =p(b-a) and nonnegative integral times. Temporal homogeneity is also assumed, and usually the initial position will be fixed at 0 (the identity of G). Letting x(n) be a typical sample function, the walk is recurrent just in case for each gCG, Pr(x(n) =g for some n) = 1. This will hold just in