Tacnode GUE-minor processes and double Aztec diamonds

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 proce...

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Bibliographic Details
Published in:Probability theory and related fields 2015-06, Vol.162 (1-2), p.275-325
Main Authors: Adler, Mark, Chhita, Sunil, Johansson, Kurt, van Moerbeke, Pierre
Format: Article
Language:English
Subjects:
Airy process
Applied mathematics
Diamonds
Dimer
Double cusps
Economics
Extended kernels
Finance
Insurance
Interlacing
Kasteleyn
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
Mining industry
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Random Hermitian ensembles
Random tiling
Statistics for Business
Studies
Theoretical
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Summary: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.
ISSN:0178-8051
1432-2064
1432-2064
DOI:10.1007/s00440-014-0573-9