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An Inductive Proof of the Berry-Esseen Theorem for Character Ratios
Jason Fulman
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
fulman@usc.edu
Annals of Combinatorics 10 (3) p.319-332 September, 2006
AMS Subject Classification: 05E10, 60C05
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.
Keywords: character ratio, Berry-Esseen theorem, Stein's method, Plancherel measure, Jack polynomial

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