Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Rectangular Young tableaux and the Jacobi ensemble
Philippe Marchal  1  
1 : Laboratoire Analyse, Géométrie et Applications  (LAGA)  -  Website
Université Paris 8, Vincennes-Saint-Denis, université Paris 13, Institut Galilée, Centre National de la Recherche Scientifique : UMR7539, Université Paris 8 Vincennes-Saint-Denis
Institut Galilée, Université Paris 13, 99 avenue Jean-Baptiste Clément, F-93430, Villetaneuse, France -  France

It has been shown by Pittel and Romik that the random surface associated with a large rectangular Young
tableau converges to a deterministic limit. We study the fluctuations from this limit along the edges of the rectangle.
We show that in the corner, these fluctuations are gaussian whereas, away from the corner and when the rectangle is
a square, the fluctuations are given by the Tracy-Widom distribution. Our method is based on a connection with the
Jacobi ensemble.

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