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Probability Theory and Related Fields

, Volume 162, Issue 1–2, pp 275–325 | Cite as

Tacnode GUE-minor processes and double Aztec diamonds

  • Mark Adler
  • Sunil Chhita
  • Kurt Johansson
  • Pierre van Moerbeke
Article

Abstract

We study determinantal point processes arising in random domino tilings of a double Aztec diamond, a region consisting of two overlapping Aztec diamonds. At a turning point in a single Aztec diamond where the disordered region touches the boundary, the natural limiting process is the GUE-minor process. Increasing the size of a double Aztec diamond while keeping the overlap between the two Aztec diamonds finite, we obtain a new determinantal point process which we call the tacnode GUE-minor process. This process can be thought of as two colliding GUE-minor processes. As part of the derivation of the particle kernel whose scaling limit naturally gives the tacnode GUE-minor process, we find the inverse Kasteleyn matrix for the dimer model version of the Double Aztec diamond.

Keywords

Interlacing Random tiling Kasteleyn Dimer  Airy process Extended kernels Random Hermitian ensembles 

Mathematics Subject Classification (2010)

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Mark Adler
    • 1
  • Sunil Chhita
    • 2
  • Kurt Johansson
    • 3
  • Pierre van Moerbeke
    • 1
    • 4
  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA
  2. 2.Institute of Applied MathematicsUniversity of BonnBonnGermany
  3. 3.Department of MathematicsRoyal Institute of Technology (KTH)StockholmSweden
  4. 4.Department of MathematicsUniversité de LouvainLouvain-la-NeuveBelgium

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