15 May 2016 Gaussian fluctuations of Young diagrams and structure constants of Jack characters
Maciej Dołęga, Valentin Féray
Duke Math. J. 165(7): 1193-1282 (15 May 2016). DOI: 10.1215/00127094-3449566


In this paper, we consider a deformation of Plancherel measure linked to Jack polynomials. Our main result is the description of the first- and second-order asymptotics of the bulk of a random Young diagram under this distribution, which extends celebrated results of Vershik, Kerov, Logan, and Shepp (for the first-order asymptotics) and Kerov (for the second-order asymptotics). This gives more evidence for the connection with the Gaussian β-ensemble, already suggested by a work of Matsumoto.

Our main tool is a polynomiality result for the structure constants of some quantities that we call Jack characters, recently introduced by Lassalle. We believe that this result is also interesting in itself and we give several other applications of it.


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Maciej Dołęga. Valentin Féray. "Gaussian fluctuations of Young diagrams and structure constants of Jack characters." Duke Math. J. 165 (7) 1193 - 1282, 15 May 2016. https://doi.org/10.1215/00127094-3449566


Received: 24 September 2014; Revised: 27 May 2015; Published: 15 May 2016
First available in Project Euclid: 4 February 2016

zbMATH: 1338.60017
MathSciNet: MR3498866
Digital Object Identifier: 10.1215/00127094-3449566

Primary: 60C05
Secondary: 05E05 , 60B20

Keywords: bulk fluctuations , Jack measure , Jack polynomials , polynomial functions on Young diagrams , Random partitions , Stein’s method

Rights: Copyright © 2016 Duke University Press


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Vol.165 • No. 7 • 15 May 2016
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