Kerov's central limit theorem for the Plancherel measure on Young diagrams

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Consider random Young diagrams with a fixed number n of boxes, where the probability distribution on diagrams is determined by the Plancherel measure. That is, the weight of a diagram is proportional to the squared dimension of the corresponding irreducible representation of the symmetric group S_n. As n goes to infinity, the boundary of the (suitably scaled) random diagram concentrates near a curve Omega (Logan-Shepp 1977, Vershik-Kerov 1977). In 1993, Kerov announced a central limit theorem describing Gaussian fluctuations of random diagrams around the limit shape Omega. Here we propose a reconstruction of his proof, largely based on Kerov's unpublished work notes (1999). We also discuss a striking similarity between Kerov's result and central limit theorems for random matrices (Diaconis-Shahshahani, Johansson).
AMS-TeX, 49 pages, no figures

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Combinatorics, Probability, Representation Theory, 05E05 (Primary) 05E10, 20C30, 20C32, 60B10, 60B15 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/66957

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304010
 http://arxiv.org/abs/math/0304010
 In: S.Fomin, editor. Symmetric Functions 2001: Surveys of Developments and Perspectives (NATO Science Series II. Mathematics, Physics and Chemistry. Vol.74), Kluwer, 2002, pp. 93-151

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