Publication: Gaussian fluctuations of Young diagrams and structure constants of Jack characters
Gaussian fluctuations of Young diagrams and structure constants of Jack characters
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Dołęga, M., & Féray, V. (2016). Gaussian fluctuations of Young diagrams and structure constants of Jack characters. Duke Mathematical Journal, 165(7), 1193–1282. https://doi.org/10.1215/00127094-3449566
Abstract
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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 $\beta$-ensemble, already suggested by a work of Matsumoto. Our main tool is a polynomiality res
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- Dołęga, Maciej
- Féray, Valentin
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Dołęga, M., & Féray, V. (2016). Gaussian fluctuations of Young diagrams and structure constants of Jack characters. Duke Mathematical Journal, 165(7), 1193–1282. https://doi.org/10.1215/00127094-3449566
