Mirjana Vuletić - The Gaussian free field and strict plane partitions

dmtcs:2364 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2364
The Gaussian free field and strict plane partitionsArticle

Authors: Mirjana Vuletić 1

  • 1 Department of Mathematics

We study height fluctuations around the limit shape of a measure on strict plane partitions. It was shown in our earlier work that this measure is a Pfaffian process. We show that the height fluctuations converge to a pullback of the Green's function for the Laplace operator with Dirichlet boundary conditions on the first quadrant. We use a Pfaffian formula for higher moments to show that the height fluctuations are governed by the Gaussian free field. The results follow from the correlation kernel asymptotics which is obtained by the steepest descent method.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Gaussian free field,Pfaffian process,limit shape,height function fluctuations,plane partitions,correlation function asymptotics,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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