Fluctuations and arctic curve in the Aztec diamond
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,...
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ftunivlouvain:oai:dial.uclouvain.be:boreal:275544 2024-05-12T07:59:04+00:00 Fluctuations and arctic curve in the Aztec diamond Debin, Bryan de Kemmeter, Jean-François Ruelle, Philippe UCL - SST/IRMP - Institut de recherche en mathématique et physique 2022 http://hdl.handle.net/2078.1/275544 eng eng boreal:275544 http://hdl.handle.net/2078.1/275544 info:eu-repo/semantics/openAccess Belgian Journal of Physics, Vol. 1, no.5, p. 18--26 (2022) info:eu-repo/semantics/article 2022 ftunivlouvain 2024-04-17T16:29:46Z 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. Article in Journal/Newspaper Arctic DIAL@UCLouvain (Université catholique de Louvain) Arctic |
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Open Polar |
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DIAL@UCLouvain (Université catholique de Louvain) |
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ftunivlouvain |
language |
English |
description |
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. |
author2 |
UCL - SST/IRMP - Institut de recherche en mathématique et physique |
format |
Article in Journal/Newspaper |
author |
Debin, Bryan de Kemmeter, Jean-François Ruelle, Philippe |
spellingShingle |
Debin, Bryan de Kemmeter, Jean-François Ruelle, Philippe Fluctuations and arctic curve in the Aztec diamond |
author_facet |
Debin, Bryan de Kemmeter, Jean-François Ruelle, Philippe |
author_sort |
Debin, Bryan |
title |
Fluctuations and arctic curve in the Aztec diamond |
title_short |
Fluctuations and arctic curve in the Aztec diamond |
title_full |
Fluctuations and arctic curve in the Aztec diamond |
title_fullStr |
Fluctuations and arctic curve in the Aztec diamond |
title_full_unstemmed |
Fluctuations and arctic curve in the Aztec diamond |
title_sort |
fluctuations and arctic curve in the aztec diamond |
publishDate |
2022 |
url |
http://hdl.handle.net/2078.1/275544 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Belgian Journal of Physics, Vol. 1, no.5, p. 18--26 (2022) |
op_relation |
boreal:275544 http://hdl.handle.net/2078.1/275544 |
op_rights |
info:eu-repo/semantics/openAccess |
_version_ |
1798839949213040640 |