An Inductive Proof of the Berry-Esseen Theorem for Character Ratios
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- Fulman, J. Ann. Comb. (2006) 10: 319. doi:10.1007/s00026-006-0290-x
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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.