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Tacnode GUE-minor processes and double Aztec diamonds.

Adler, Mark and Chhita, Sunil and Johansson, Kurt and van Moerbeke, Pierre (2014) 'Tacnode GUE-minor processes and double Aztec diamonds.', Probability theory and related fields., 162 (1). pp. 275-325.


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.

Item Type:Article
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Date accepted:23 May 2014
Date deposited:24 November 2016
Date of first online publication:25 July 2014
Date first made open access:No date available

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