Representation theory and cycle statistics for random walks on the symmetric group

Dominic Arcona

Paper

Representation theory and cycle statistics for random walks on the symmetric group

Abstract

We use representation theory of

to analyze the mixing of permutation cycle type statistics

{# of

-cycles of

} for any fixed

and

resulting from a random

-cycle walk on

. We also derive analogous results for the random star transposition walk. Our approach uses the method of moments; a key ingredient is a new formula for the coefficients in the irreducible character decomposition of the

-class function

for any positive integers

when