Concavity analysis of the tangent method
The tangent method has recently been devised by Colomo and Sportiello (2016 J. Stat. Phys. 164 1488–523) as an efficient way to determine the shape of arctic curves. Largely conjectural, it has been tested successfully in a variety of models. However no proof and no general geometric insight have...
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Online Access: | http://hdl.handle.net/2078.1/222707 https://doi.org/10.1088/1742-5468/ab43d6 |
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ftunistlouisbrus:oai:dial.uclouvain.be:boreal:222707 2024-05-12T07:59:16+00:00 Concavity analysis of the tangent method Debin, Bryan Granet, Etienne Ruelle, Philippe UCL - SST/IRMP - Institut de recherche en mathématique et physique 2019 http://hdl.handle.net/2078.1/222707 https://doi.org/10.1088/1742-5468/ab43d6 eng eng Institute of Physics Publishing Ltd. boreal:222707 http://hdl.handle.net/2078.1/222707 doi:10.1088/1742-5468/ab43d6 urn:EISSN:1742-5468 info:eu-repo/semantics/openAccess Journal of Statistical Mechanics: Theory and Experiment, Vol. , no., p. 113107 (2019) solvable lattice models arctic curves info:eu-repo/semantics/article 2019 ftunistlouisbrus https://doi.org/10.1088/1742-5468/ab43d6 2024-04-18T17:25:06Z The tangent method has recently been devised by Colomo and Sportiello (2016 J. Stat. Phys. 164 1488–523) as an efficient way to determine the shape of arctic curves. Largely conjectural, it has been tested successfully in a variety of models. However no proof and no general geometric insight have been given so far, either to show its validity or to allow for an understanding of why the method actually works. In this paper, we propose a universal framework which accounts for the tangency part of the tangent method, whenever a formulation in terms of directed lattice paths is available. Our analysis shows that the key factor responsible for the tangency property is the concavity of the entropy (also called the Lagrangean function) of long random lattice paths. We extend the proof of the tangency to q-deformed paths. Article in Journal/Newspaper Arctic DIAL@USL-B (Université Saint-Louis, Bruxelles) Arctic Journal of Statistical Mechanics: Theory and Experiment 2019 11 113107 |
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Open Polar |
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DIAL@USL-B (Université Saint-Louis, Bruxelles) |
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ftunistlouisbrus |
language |
English |
topic |
solvable lattice models arctic curves |
spellingShingle |
solvable lattice models arctic curves Debin, Bryan Granet, Etienne Ruelle, Philippe Concavity analysis of the tangent method |
topic_facet |
solvable lattice models arctic curves |
description |
The tangent method has recently been devised by Colomo and Sportiello (2016 J. Stat. Phys. 164 1488–523) as an efficient way to determine the shape of arctic curves. Largely conjectural, it has been tested successfully in a variety of models. However no proof and no general geometric insight have been given so far, either to show its validity or to allow for an understanding of why the method actually works. In this paper, we propose a universal framework which accounts for the tangency part of the tangent method, whenever a formulation in terms of directed lattice paths is available. Our analysis shows that the key factor responsible for the tangency property is the concavity of the entropy (also called the Lagrangean function) of long random lattice paths. We extend the proof of the tangency to q-deformed paths. |
author2 |
UCL - SST/IRMP - Institut de recherche en mathématique et physique |
format |
Article in Journal/Newspaper |
author |
Debin, Bryan Granet, Etienne Ruelle, Philippe |
author_facet |
Debin, Bryan Granet, Etienne Ruelle, Philippe |
author_sort |
Debin, Bryan |
title |
Concavity analysis of the tangent method |
title_short |
Concavity analysis of the tangent method |
title_full |
Concavity analysis of the tangent method |
title_fullStr |
Concavity analysis of the tangent method |
title_full_unstemmed |
Concavity analysis of the tangent method |
title_sort |
concavity analysis of the tangent method |
publisher |
Institute of Physics Publishing Ltd. |
publishDate |
2019 |
url |
http://hdl.handle.net/2078.1/222707 https://doi.org/10.1088/1742-5468/ab43d6 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Journal of Statistical Mechanics: Theory and Experiment, Vol. , no., p. 113107 (2019) |
op_relation |
boreal:222707 http://hdl.handle.net/2078.1/222707 doi:10.1088/1742-5468/ab43d6 urn:EISSN:1742-5468 |
op_rights |
info:eu-repo/semantics/openAccess |
op_doi |
https://doi.org/10.1088/1742-5468/ab43d6 |
container_title |
Journal of Statistical Mechanics: Theory and Experiment |
container_volume |
2019 |
container_issue |
11 |
container_start_page |
113107 |
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1798840389314019328 |