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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Vydáno v:Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th...
Hlavní autor: Marchal, Philippe
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: DMTCS 22.04.2020
Discrete Mathematics & Theoretical Computer Science
Témata:
[math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
Combinatorics
ISSN:1365-8050, 1462-7264, 1365-8050
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Popis
Shrnutí: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