Annals of Combinatorics

, Volume 10, Issue 3, pp 319–332

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


DOI: 10.1007/s00026-006-0290-x

Cite this article as:
Fulman, J. Ann. Comb. (2006) 10: 319. doi:10.1007/s00026-006-0290-x


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.



character ratioBerry-Esseen theoremStein’s methodPlancherel measureJack polynomial

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA