Random walks on wreath products of groups

2000/06/16 by Jr. Schoolfield, Schoolfield,, Clyde H.
Mathematics · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.math/0006118

Abstract

We bound the rate of convergence to uniformity for certain random walks on the complete monomial groups G \wr S_n for any group G. These results provide rates of convergence for random walks on a number of groups of interest: the hyperoctahedral group Z₂ \wr S_n, the generalized symmetric group Z_m \wr S_n, and S_m \wr S_n. These results provide benchmarks to which many other random walks, modeling a wide range of phenomena, may be compared using the comparison technique, thereby yielding bounds on the rates of convergence to uniformity for previously intractable random walks.

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