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 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Airy process

Dimer

Extended kernels

Interlacing

Kasteleyn

Random Hermitian ensembles

Random tiling

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