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

Mathematics – Combinatorics

Scientific paper

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revised version (main modification to the proof of Theorem 2.5)

Scientific paper

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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