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Fluctuations and arctic curve in the Aztec diamond | | Bryan Debin
; Jean-François de Kemmeter
; Philippe Ruelle
; | | Date: |
2 Jan 2023 | | Abstract: | Domino tilings of Aztec diamonds are known to exhibit an arctic phenomenon,
namely a separation between frozen regions (in which all the dominoes have the
same orientation) and a central disordered region (where dominoes are found
without any apparent order). This separation was proved to converge, under a
suitable rescaling, to the Airy process whose $1$-point distribution is the
Tracy-Widom distribution. In this work, we conjecture, by means of numerical
analysis, that the boundary between the frozen and disordered regions,
converges, for the same rescaling, to the Airy line ensemble, a generalisation
of the Airy process. | | Source: | arXiv, 2301.00600 | | Services: | Forum | Review | PDF | Favorites | |
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