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Martingales and character ratios |
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| Authors: | Jason Fulman |
| Affiliation: | Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 |
| 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. |
| Keywords: | Martingale central limit theorem character ratio symmetric group Jack polynomial |
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