Annals of Combinatorics

, Volume 10, Issue 3, pp 319-332

First online:

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

  • Jason FulmanAffiliated withDepartment of Mathematics, University of Southern California Email author 

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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.

AMS Subject Classification.

05E10 60C05


character ratio Berry-Esseen theorem Stein’s method Plancherel measure Jack polynomial