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Martingales and character ratios

Author(s): Jason Fulman
Journal: Trans. Amer. Math. Soc. 358 (2006), 4533-4552.
MSC (2000): Primary 05E10; Secondary 60C05
Posted: April 11, 2006
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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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Additional Information:

Jason Fulman
Affiliation: Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: fulman@math.pitt.edu

DOI: 10.1090/S0002-9947-06-03865-7
PII: S 0002-9947(06)03865-7
Keywords: Martingale, central limit theorem, character ratio, symmetric group, Jack polynomial
Received by editor(s): February 25, 2004
Received by editor(s) in revised form: September 21, 2004
Posted: April 11, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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