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Tilings of Non-conv...
Tilings of Non-convex Polygons, Skew-Young Tableaux and Determinantal Processes
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- Adler, Mark (author)
- Brandeis Univ, Dept Math, Waltham, MA 02453 USA.
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- Johansson, Kurt, 1960- (author)
- KTH,Matematik (Inst.)
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- van Moerbeke, Pierre (author)
- Univ Louvain, Dept Math, B-1348 Louvain, Belgium.;Brandeis Univ, Waltham, MA 02453 USA.
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Brandeis Univ, Dept Math, Waltham, MA 02453 USA Matematik (Inst.) (creator_code:org_t)
- 2018-07-28
- 2018
- English.
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In: Communications in Mathematical Physics. - : Springer. - 0010-3616 .- 1432-0916. ; 364:1, s. 287-342
- Related links:
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http://arxiv.org/pdf...
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Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Fysik -- Annan fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Other Physics Topics (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
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