Arctic Curves In Path Models from The Tangent Method
International audience Recently, Colomo and Sportiello introduced a powerful method, known as the $Tangent\ Method$, for computing the arctic curve in statistical models which have a (non-or weakly-) intersecting lattice path formulation. We apply the Tangent Method to compute arctic curves in vario...
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ftceafr:oai:HAL:cea-01692535v1 2024-09-09T19:17:45+00:00 Arctic Curves In Path Models from The Tangent Method Di Francesco, Philippe Lapa, Matthew, F. Institut de Physique Théorique - UMR CNRS 3681 (IPHT) Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA) Department of Mathematics Urbana University of Illinois at Urbana-Champaign Urbana (UIUC) University of Illinois System-University of Illinois System 2018 https://cea.hal.science/cea-01692535 https://cea.hal.science/cea-01692535/document https://cea.hal.science/cea-01692535/file/1711.03182.pdf https://doi.org/10.1088/1751-8121/aab3c0 en eng HAL CCSD IOP Publishing info:eu-repo/semantics/altIdentifier/arxiv/1711.03182 info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/aab3c0 cea-01692535 https://cea.hal.science/cea-01692535 https://cea.hal.science/cea-01692535/document https://cea.hal.science/cea-01692535/file/1711.03182.pdf ARXIV: 1711.03182 doi:10.1088/1751-8121/aab3c0 info:eu-repo/semantics/OpenAccess ISSN: 1751-8113 EISSN: 1751-8121 Journal of Physics A: Mathematical and Theoretical https://cea.hal.science/cea-01692535 Journal of Physics A: Mathematical and Theoretical, 2018, 51, pp.155202. ⟨10.1088/1751-8121/aab3c0⟩ [PHYS]Physics [physics] info:eu-repo/semantics/article Journal articles 2018 ftceafr https://doi.org/10.1088/1751-8121/aab3c0 2024-07-22T13:27:40Z International audience Recently, Colomo and Sportiello introduced a powerful method, known as the $Tangent\ Method$, for computing the arctic curve in statistical models which have a (non-or weakly-) intersecting lattice path formulation. We apply the Tangent Method to compute arctic curves in various models: the domino tiling of the Aztec diamond for which we recover the celebrated arctic circle; a model of Dyck paths equivalent to the rhombus tiling of a half-hexagon for which we find an arctic half-ellipse; another rhombus tiling model with an arctic parabola; the vertically symmetric alternating sign matrices, where we find the same arctic curve as for unconstrained alternating sign matrices. The latter case involves lattice paths that are non-intersecting but that are allowed to have osculating contact points, for which the Tangent Method was argued to still apply. For each problem we estimate the large size asymptotics of a certain one-point function using LU decomposition of the corresponding Gessel-Viennot matrices, and a reformulation of the result amenable to asymptotic analysis. Article in Journal/Newspaper Arctic HAL-CEA (Commissariat à l'énergie atomique et aux énergies alternatives) Arctic Journal of Physics A: Mathematical and Theoretical 51 15 155202 |
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HAL-CEA (Commissariat à l'énergie atomique et aux énergies alternatives) |
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language |
English |
topic |
[PHYS]Physics [physics] |
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[PHYS]Physics [physics] Di Francesco, Philippe Lapa, Matthew, F. Arctic Curves In Path Models from The Tangent Method |
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[PHYS]Physics [physics] |
description |
International audience Recently, Colomo and Sportiello introduced a powerful method, known as the $Tangent\ Method$, for computing the arctic curve in statistical models which have a (non-or weakly-) intersecting lattice path formulation. We apply the Tangent Method to compute arctic curves in various models: the domino tiling of the Aztec diamond for which we recover the celebrated arctic circle; a model of Dyck paths equivalent to the rhombus tiling of a half-hexagon for which we find an arctic half-ellipse; another rhombus tiling model with an arctic parabola; the vertically symmetric alternating sign matrices, where we find the same arctic curve as for unconstrained alternating sign matrices. The latter case involves lattice paths that are non-intersecting but that are allowed to have osculating contact points, for which the Tangent Method was argued to still apply. For each problem we estimate the large size asymptotics of a certain one-point function using LU decomposition of the corresponding Gessel-Viennot matrices, and a reformulation of the result amenable to asymptotic analysis. |
author2 |
Institut de Physique Théorique - UMR CNRS 3681 (IPHT) Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA) Department of Mathematics Urbana University of Illinois at Urbana-Champaign Urbana (UIUC) University of Illinois System-University of Illinois System |
format |
Article in Journal/Newspaper |
author |
Di Francesco, Philippe Lapa, Matthew, F. |
author_facet |
Di Francesco, Philippe Lapa, Matthew, F. |
author_sort |
Di Francesco, Philippe |
title |
Arctic Curves In Path Models from The Tangent Method |
title_short |
Arctic Curves In Path Models from The Tangent Method |
title_full |
Arctic Curves In Path Models from The Tangent Method |
title_fullStr |
Arctic Curves In Path Models from The Tangent Method |
title_full_unstemmed |
Arctic Curves In Path Models from The Tangent Method |
title_sort |
arctic curves in path models from the tangent method |
publisher |
HAL CCSD |
publishDate |
2018 |
url |
https://cea.hal.science/cea-01692535 https://cea.hal.science/cea-01692535/document https://cea.hal.science/cea-01692535/file/1711.03182.pdf https://doi.org/10.1088/1751-8121/aab3c0 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
ISSN: 1751-8113 EISSN: 1751-8121 Journal of Physics A: Mathematical and Theoretical https://cea.hal.science/cea-01692535 Journal of Physics A: Mathematical and Theoretical, 2018, 51, pp.155202. ⟨10.1088/1751-8121/aab3c0⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/arxiv/1711.03182 info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/aab3c0 cea-01692535 https://cea.hal.science/cea-01692535 https://cea.hal.science/cea-01692535/document https://cea.hal.science/cea-01692535/file/1711.03182.pdf ARXIV: 1711.03182 doi:10.1088/1751-8121/aab3c0 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1088/1751-8121/aab3c0 |
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Journal of Physics A: Mathematical and Theoretical |
container_volume |
51 |
container_issue |
15 |
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155202 |
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