A comparison theorem on convergence rates of random walks on groups (Q1210343)

Let \(G\) be a compact Hausdorff group. The comparison theorem given in the paper gives a partial answer to the following question: what is tendency of the change in the convergence rate when we enlarge the support of probability that generates a random walk, and/or change the original mass assignment? As applications of the comparison theorem the authors consider random walks on a finite cyclic group \(Z(n)\), on a hypercube \(Z^ n(2)\), on the one-dimensional torus \(T\) and some other examples.