Lozenge tilings with free boundary
We study tilings with lozenges of a domain with free boundary conditions on one side. These correspondto boxed symmetric plane partitions. We show that the positions of the horizontal lozenges near the left flatboundary, in the limit, have the same joint distribution as the eigenvalues from a Gaussi...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2015-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2474/pdf |
| _version_ | 1827323930102202368 |
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| author | Greta Panova |
| author_facet | Greta Panova |
| author_sort | Greta Panova |
| collection | DOAJ |
| description | We study tilings with lozenges of a domain with free boundary conditions on one side. These correspondto boxed symmetric plane partitions. We show that the positions of the horizontal lozenges near the left flatboundary, in the limit, have the same joint distribution as the eigenvalues from a Gaussian Unitary Ensemble (theGUE-corners/minors process). We also prove the existence of a limit shape of the height function (the symmetricplane partition). We also consider domains where the sides converge to $\infty$ at different rates and recover again theGUE-corners process. |
| first_indexed | 2024-04-25T02:00:29Z |
| format | Article |
| id | doaj.art-53b54033651f47c4a120826c43faffd5 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:29Z |
| publishDate | 2015-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-53b54033651f47c4a120826c43faffd52024-03-07T15:01:26ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502015-01-01DMTCS Proceedings, 27th...Proceedings10.46298/dmtcs.24742474Lozenge tilings with free boundaryGreta Panova0University of PennsylvaniaWe study tilings with lozenges of a domain with free boundary conditions on one side. These correspondto boxed symmetric plane partitions. We show that the positions of the horizontal lozenges near the left flatboundary, in the limit, have the same joint distribution as the eigenvalues from a Gaussian Unitary Ensemble (theGUE-corners/minors process). We also prove the existence of a limit shape of the height function (the symmetricplane partition). We also consider domains where the sides converge to $\infty$ at different rates and recover again theGUE-corners process.https://dmtcs.episciences.org/2474/pdflozenge tilingssymmetric plane partitionslimit shapesgue eigenvalues[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Greta Panova Lozenge tilings with free boundary Discrete Mathematics & Theoretical Computer Science lozenge tilings symmetric plane partitions limit shapes gue eigenvalues [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Lozenge tilings with free boundary |
| title_full | Lozenge tilings with free boundary |
| title_fullStr | Lozenge tilings with free boundary |
| title_full_unstemmed | Lozenge tilings with free boundary |
| title_short | Lozenge tilings with free boundary |
| title_sort | lozenge tilings with free boundary |
| topic | lozenge tilings symmetric plane partitions limit shapes gue eigenvalues [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2474/pdf |
| work_keys_str_mv | AT gretapanova lozengetilingswithfreeboundary |