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Martingales and character ratios

Jason Fulman
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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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Jason Fulman. 2004-02-25. Martingales and character ratios. https://arxiv.org/abs/math/0402409

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