Double Aztec diamonds and the tacnode process |
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Authors: | Mark Adler Kurt Johansson Pierre van Moerbeke |
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Institution: | 1. Department of Mathematics, Brandeis University, Waltham, MA 02453, USA;2. Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden;3. Department of Mathematics, Université de Louvain, 1348 Louvain-la-Neuve, Belgium;4. Brandeis University, Waltham, MA 02453, USA |
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Abstract: | Discrete and continuous non-intersecting random processes have given rise to critical “infinite-dimensional diffusions”, like the Airy process, the Pearcey process and variations thereof. It has been known that domino tilings of very large Aztec diamonds lead macroscopically to a disordered region within an inscribed ellipse (arctic circle in the homogeneous case), and a regular brick-like region outside the ellipse. The fluctuations near the ellipse, appropriately magnified and away from the boundary of the Aztec diamond, form an Airy process, run with time tangential to the boundary. |
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Keywords: | primary 60G60 60G65 35Q53 secondary 60G10 35Q58 |
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