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

Jason Fulman
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Abstract

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.

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Jason Fulman. 2006-08-08. An Inductive Proof of the Berry-Esseen Theorem for Character Ratios. https://arxiv.org/abs/math/0503227

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