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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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/6417/pdf |
| _version_ | 1827323930934771712 |
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| author | Philippe Marchal |
| author_facet | Philippe Marchal |
| author_sort | Philippe Marchal |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:00:30Z |
| format | Article |
| id | doaj.art-576fcb402c0143ebb94a77486d61d6e4 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:30Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-576fcb402c0143ebb94a77486d61d6e42024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.64176417Rectangular Young tableaux and the Jacobi ensemblePhilippe Marchal0Laboratoire Analyse, Géométrie et ApplicationsIt 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.https://dmtcs.episciences.org/6417/pdfcombinatorics[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Philippe Marchal Rectangular Young tableaux and the Jacobi ensemble Discrete Mathematics & Theoretical Computer Science combinatorics [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Rectangular Young tableaux and the Jacobi ensemble |
| title_full | Rectangular Young tableaux and the Jacobi ensemble |
| title_fullStr | Rectangular Young tableaux and the Jacobi ensemble |
| title_full_unstemmed | Rectangular Young tableaux and the Jacobi ensemble |
| title_short | Rectangular Young tableaux and the Jacobi ensemble |
| title_sort | rectangular young tableaux and the jacobi ensemble |
| topic | combinatorics [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6417/pdf |
| work_keys_str_mv | AT philippemarchal rectangularyoungtableauxandthejacobiensemble |