Lifting Markov chains to random walks on groups

Abstract

The determination of a Markov chain which can be lifted to a random walk on an abelian group or a group whose probability measure is a class function, is described. The analysis is facilitated whenever the probability measure on the group is a class function. A special case is that of an abelian group where any probability measure is a class function. The results show that the Fourier analysis using group representations simplifies to computations involving the irreducible characters of the group.