Tacnode GUE-minor processes and double Aztec Diamonds

Adler, Mark;Chhita, Sunil;Johansson, Kurt;Van Moerbeke, Pierre
(2015) Probability Theory and Related Fields — Vol. 162, n° 1-2, p. 275-325 (2015)

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Authors
  • Adler, MarkUCLouvain
    Author
  • Chhita, SunilUCLouvain
    Author
  • Johansson, KurtUCLouvain
    Author
  • Van Moerbeke, PierreUCLouvain
    Author
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.
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Adler, M., Chhita, S., Johansson, K., & Van Moerbeke, P. (2015). Tacnode GUE-minor processes and double Aztec Diamonds. Probability Theory and Related Fields, 162(1-2), 275-325. https://doi.org/10.1007/s00440-014-0573-9 (Original work published 2015)