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Stein's method and Plancherel measure of the symmetric group


Author: Jason Fulman
Translated by:
Journal: Trans. Amer. Math. Soc. 357 (2005), 555-570
MSC (2000): Primary 05E10; Secondary 60C05
DOI: https://doi.org/10.1090/S0002-9947-04-03499-3
Published electronically: February 4, 2004
MathSciNet review: 2095623
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Abstract: We initiate a Stein's method approach to the study of the Plancherel measure of the symmetric group. A new proof of Kerov's central limit theorem for character ratios of random representations of the symmetric group on transpositions is obtained; the proof gives an error term. The construction of an exchangeable pair needed for applying Stein's method arises from the theory of harmonic functions on Bratelli diagrams. We also find the spectrum of the Markov chain on partitions underlying the construction of the exchangeable pair. This yields an intriguing method for studying the asymptotic decomposition of tensor powers of some representations of the symmetric group.


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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9947-04-03499-3
Keywords: Plancherel measure, Stein's method, character ratio, Markov chain
Received by editor(s): May 28, 2003
Received by editor(s) in revised form: July 7, 2003
Published electronically: February 4, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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