An Inductive Proof of the Berry-Esseen Theorem for Character Ratios

Jason Fulman

Published 2005-03-11, updated 2006-08-08Version 2

Bolthausen used a variation of Stein's method to give an inductive proof of the Berry-Esseen theorem for sums of independent, identically distributed random variables. We modify this technique to prove a Berry-Esseen theorem for character ratios of a random representation of the symmetric group on transpositions. An analogous result is proved for Jack measure on partitions.