Mark Adler
Tacnode GUE-minor processes and double Aztec Diamonds
Adler, Mark; Chhita, Sunil; Johansson, Kurt; van Moerbeke, Pierre
Authors
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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Copyright Statement
The final publication is available at Springer via https://doi.org/10.1007/s00440-014-0573-9
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