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Tacnode GUE-minor processes and double Aztec Diamonds

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Adler, Mark [UCL] Chhita, Sunil [UCL] Johansson, Kurt [UCL] Van Moerbeke, Pierre [UCL]

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2015
Language Anglais
Journal information "Probability Theory and Related Fields" - Vol. 162, no. 1-2, p. 275-325 (2015)
Peer reviewed yes
Publisher Springer
issn 0178-8051
e-issn 1432-2064
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Keywords Interlacing ; Random tiling ; Kasteleyn ; Dimer ; Airy process ; Extended kernels ; Random Hermitian ensembles
Links
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Bibliographic reference Adler, Mark ; Chhita, Sunil ; Johansson, Kurt ; Van Moerbeke, Pierre. Tacnode GUE-minor processes and double Aztec Diamonds. In: Probability Theory and Related Fields, Vol. 162, no. 1-2, p. 275-325 (2015)
Permanent URL http://hdl.handle.net/2078.1/168580