A law of the iterated logarithm for Markov chains on ℕ0 associated with orthogonal polynomials

We derive laws of the iterated logarithm for Markov chains on the nonnegative integers whose transition probabilities are associated with a sequence of orthogonal polynomials. These laws can be applied to a large class of birth and death random walks and random walks on polynomial hypergroups. In particular, the results of our paper lead immediately to a law of the iterated logarithm for the growth of the distance of isotropic random walks on infinite distance-transitive graphs as well as on certain finitely generated semigroups from their starting points.