Tacnode GUE-minor processes and double Aztec diamonds

• 成果类型: Article
• 署名作者: Adler, Mark; Chhita, Sunil; Johansson, Kurt; van Moerbeke, Pierre
• 署名单位: Brandeis University; University of Bonn; Royal Institute of Technology; Universite Catholique Louvain
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-014-0573-9
• 发表日期: 2015
• 页码: 275-325
• 关键词: lattice; statistics; tilings

摘要

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.