Martingales and character ratios
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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.References
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Additional Information
- Jason Fulman
- Affiliation: Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- MR Author ID: 332245
- Email: fulman@math.pitt.edu
- Received by editor(s): February 25, 2004
- Received by editor(s) in revised form: September 21, 2004
- Published electronically: April 11, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 4533-4552
- MSC (2000): Primary 05E10; Secondary 60C05
- DOI: https://doi.org/10.1090/S0002-9947-06-03865-7
- MathSciNet review: 2231387