Annals of Combinatorics

, Volume 10, Issue 3, pp 319–332 | Cite as

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



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 


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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

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