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Tacnode GUE-minor processes and double Aztec diamonds
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2943-7006
2015 (English)In: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 162, no 1-2, 275-325 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2015. Vol. 162, no 1-2, 275-325 p.
Keyword [en]
Airy process, Dimer, Extended kernels, Interlacing, Kasteleyn, Random Hermitian ensembles, Random tiling
National Category
URN: urn:nbn:se:kth:diva-170337DOI: 10.1007/s00440-014-0573-9ISI: 000355182400008ScopusID: 2-s2.0-84929957197OAI: diva2:827663
Knut and Alice Wallenberg Foundation, KAW 2010.0063Swedish Research Council

QC 20150629

Available from: 2015-06-29 Created: 2015-06-29 Last updated: 2015-08-17Bibliographically approved

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