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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2020

Rectangular Young tableaux and the Jacobi ensemble

Philippe Marchal

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 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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Dates and versions

hal-01217954 , version 1 (22-10-2015)
hal-01217954 , version 2 (26-06-2019)

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Philippe Marchal. Rectangular Young tableaux and the Jacobi ensemble. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6417⟩. ⟨hal-01217954v2⟩
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