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Tilings of Non-convex Polygons, Skew-Young Tableaux and Determinantal Processes
Brandeis Univ, Dept Math, Waltham, MA 02453 USA..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-2943-7006
Univ Louvain, Dept Math, B-1348 Louvain, Belgium.;Brandeis Univ, Waltham, MA 02453 USA..
2018 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 364, no 1, p. 287-342Article in journal (Refereed) Published
Abstract [en]

This paper studies random lozenge tilings of general non-convex polygonal regions. We show that the pairwise interaction of the non-convexities leads asymptotically to new kernels and thus to new statistics for the tiling fluctuations. The precise geometrical figure here consists of a hexagon with cuts along opposite edges. For this model, we take limits when the size of the hexagon and the cuts tend to infinity, while keeping certain geometric data fixed in order to guarantee sufficient interaction between the cuts in the limit. We show in this paper that the kernel for the finite tiling model can be expressed as a multiple integral, where the number of integrations is related to the fixed geometric data above. The limiting kernel is believed to be a universal master kernel.

Place, publisher, year, edition, pages
Springer, 2018. Vol. 364, no 1, p. 287-342
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-237085DOI: 10.1007/s00220-018-3168-yISI: 000446534900008Scopus ID: 2-s2.0-85044153709OAI: oai:DiVA.org:kth-237085DiVA, id: diva2:1258231
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation, KAW 2010.0063
Note

QC 20181024

Available from: 2018-10-24 Created: 2018-10-24 Last updated: 2018-10-24Bibliographically approved

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