Lozenge Tilings of Hexagons with Cuts and Asymptotic Fluctuations: a New Universality Class

  • Mark Adler
  • Kurt Johansson
  • Pierre van Moerbeke


This paper investigates lozenge tilings of non-convex hexagonal regions and more specifically the asymptotic fluctuations of the tilings within and near the strip formed by opposite cuts in the regions, when the size of the regions tend to infinity, together with the cuts. It leads to a new kernel, which is expected to have universality properties.


Lozenge tilings Non-convex polygons Kernels Asymptotics 

Mathematics Subject Classification (2010)

Primary: 60G60 60G65 35Q53 Secondary: 60G10 35Q58 


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Mark Adler
    • 1
  • Kurt Johansson
    • 2
  • Pierre van Moerbeke
    • 1
    • 3
  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA
  2. 2.Department of MathematicsKTH Royal Institute of TechnologyStockholmSweden
  3. 3.Department of MathematicsUniversité de LouvainLouvain-la-NeuveBelgium

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