Martingales and character ratios

Fulman, Jason

doi:10.1090/S0002-9947-06-03865-7

Martingales and character ratios
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Trans. Amer. Math. Soc. 358 (2006), 4533-4552 Request permission

Abstract:

Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the symmetric group on transpositions. A generalization of these results is given for Jack measure on partitions. We also give a probabilistic proof of a result of Burnside and Brauer on the decomposition of tensor products.

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