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Tacnode GUE-minor processes and double Aztec Diamonds

Adler, Mark; Chhita, Sunil; Johansson, Kurt; van Moerbeke, Pierre

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Authors

Mark Adler

Kurt Johansson

Pierre van Moerbeke



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.

Citation

Adler, M., Chhita, S., Johansson, K., & van Moerbeke, P. (2014). Tacnode GUE-minor processes and double Aztec Diamonds. Probability Theory and Related Fields, 162(1), 275-325. https://doi.org/10.1007/s00440-014-0573-9

Journal Article Type Article
Acceptance Date May 23, 2014
Online Publication Date Jul 25, 2014
Publication Date Jul 25, 2014
Deposit Date Oct 12, 2016
Publicly Available Date Nov 24, 2016
Journal Probability Theory and Related Fields
Print ISSN 0178-8051
Electronic ISSN 1432-2064
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 162
Issue 1
Pages 275-325
DOI https://doi.org/10.1007/s00440-014-0573-9

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