Random walk on finite extensions of lattices

We obtain a precise formula for the probability that a random walker returns to the origin after n steps on some semi-direct product groups obtained by extending a Euclidean lattice by a finite group. Prior to this work, to the best of our knowledge, for the class of groups considered, only asymptotic estimates were available in the literature.

We obtain a precise formula for the probability that a random walker returns to the origin after n steps on some semi-direct product groups obtained by extending a Euclidean lattice by a finite group. Prior to this work, to the best of our knowledge, for the class of groups considered, only asymptotic estimates were available in the literature.

random walk semidirect groups -nite extension

random walk semidirect groups -nite extension