Rectangular Young tableaux and the Jacobi ensemble

It has been shown by Pittel and Romik that the random surface associated with a large rectangular Youngtableau 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...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 28th...
Main Author: Marchal, Philippe
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 22.04.2020
Discrete Mathematics & Theoretical Computer Science
Subjects:
[math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
Combinatorics
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary:It has been shown by Pittel and Romik that the random surface associated with a large rectangular Youngtableau 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 isa square, the fluctuations are given by the Tracy-Widom distribution. Our method is based on a connection with theJacobi ensemble.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.6417