Rectangular Young tableaux and the Jacobi ensemble

2015/10/22 by Philippe Marchal, Marchal, Philippe
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1510.06598

arxiv created 2015/10/22 · arxiv updated 2015/10/23

Abstract

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 wheras, 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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