Greta Panova - Lozenge tilings with free boundary

dmtcs:2474 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2474
Lozenge tilings with free boundaryArticle

Authors: Greta Panova 1

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.


Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: lozenge tilings,symmetric plane partitions,limit shapes,GUE eigenvalues,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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