An Inductive Proof of the Berry-Esseen Theorem for Character Ratios
Abstract
Description
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.
revised version (main modification to the proof of Theorem 2.5)
revised version (main modification to the proof of Theorem 2.5)