Arctic curves for paths with arbitrary starting points: a tangent method approach
International audience We use the tangent method of Colomo and Sportiello to investigate the arctic curve in a model of non-intersecting lattice paths with arbitrary fixed starting points aligned along some boundary and whose distribution is characterized by some arbitrary piecewise differentiable f...
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ftceafr:oai:HAL:cea-02011867v1 2024-09-09T19:18:00+00:00 Arctic curves for paths with arbitrary starting points: a tangent method approach Di Francesco, Philippe Guitter, Emmanuel 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, Illinois State University Illinois State University ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014) 2018-08-31 https://cea.hal.science/cea-02011867 https://cea.hal.science/cea-02011867/document https://cea.hal.science/cea-02011867/file/gUITT.pdf https://doi.org/10.1088/1751-8121/aad028 en eng HAL CCSD IOP Publishing info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/aad028 cea-02011867 https://cea.hal.science/cea-02011867 https://cea.hal.science/cea-02011867/document https://cea.hal.science/cea-02011867/file/gUITT.pdf doi:10.1088/1751-8121/aad028 info:eu-repo/semantics/OpenAccess ISSN: 1751-8113 EISSN: 1751-8121 Journal of Physics A: Mathematical and Theoretical https://cea.hal.science/cea-02011867 Journal of Physics A: Mathematical and Theoretical, 2018, 51, pp.355201. ⟨10.1088/1751-8121/aad028⟩ [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] info:eu-repo/semantics/article Journal articles 2018 ftceafr https://doi.org/10.1088/1751-8121/aad028 2024-07-22T13:24:32Z International audience We use the tangent method of Colomo and Sportiello to investigate the arctic curve in a model of non-intersecting lattice paths with arbitrary fixed starting points aligned along some boundary and whose distribution is characterized by some arbitrary piecewise differentiable function. We find that the arctic curve has a simple explicit parametric representation depending of this function, providing us with a simple transform that maps the arbitrary boundary condition to the arctic curve location. We discuss generic starting point distributions as well as particular freezing ones which create additional frozen domains adjacent to the boundary, hence new portions for the arctic curve. A number of examples are presented, corresponding to both generic and freezing distributions. Our results corroborate already known expressions obtained by more involved methods based on bulk correlations, hence providing more evidence to the validity of the tangent method. 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 35 355201 |
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HAL-CEA (Commissariat à l'énergie atomique et aux énergies alternatives) |
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English |
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[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] |
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[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Di Francesco, Philippe Guitter, Emmanuel Arctic curves for paths with arbitrary starting points: a tangent method approach |
topic_facet |
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] |
description |
International audience We use the tangent method of Colomo and Sportiello to investigate the arctic curve in a model of non-intersecting lattice paths with arbitrary fixed starting points aligned along some boundary and whose distribution is characterized by some arbitrary piecewise differentiable function. We find that the arctic curve has a simple explicit parametric representation depending of this function, providing us with a simple transform that maps the arbitrary boundary condition to the arctic curve location. We discuss generic starting point distributions as well as particular freezing ones which create additional frozen domains adjacent to the boundary, hence new portions for the arctic curve. A number of examples are presented, corresponding to both generic and freezing distributions. Our results corroborate already known expressions obtained by more involved methods based on bulk correlations, hence providing more evidence to the validity of the tangent method. |
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, Illinois State University Illinois State University ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014) |
format |
Article in Journal/Newspaper |
author |
Di Francesco, Philippe Guitter, Emmanuel |
author_facet |
Di Francesco, Philippe Guitter, Emmanuel |
author_sort |
Di Francesco, Philippe |
title |
Arctic curves for paths with arbitrary starting points: a tangent method approach |
title_short |
Arctic curves for paths with arbitrary starting points: a tangent method approach |
title_full |
Arctic curves for paths with arbitrary starting points: a tangent method approach |
title_fullStr |
Arctic curves for paths with arbitrary starting points: a tangent method approach |
title_full_unstemmed |
Arctic curves for paths with arbitrary starting points: a tangent method approach |
title_sort |
arctic curves for paths with arbitrary starting points: a tangent method approach |
publisher |
HAL CCSD |
publishDate |
2018 |
url |
https://cea.hal.science/cea-02011867 https://cea.hal.science/cea-02011867/document https://cea.hal.science/cea-02011867/file/gUITT.pdf https://doi.org/10.1088/1751-8121/aad028 |
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-02011867 Journal of Physics A: Mathematical and Theoretical, 2018, 51, pp.355201. ⟨10.1088/1751-8121/aad028⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/aad028 cea-02011867 https://cea.hal.science/cea-02011867 https://cea.hal.science/cea-02011867/document https://cea.hal.science/cea-02011867/file/gUITT.pdf doi:10.1088/1751-8121/aad028 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1088/1751-8121/aad028 |
container_title |
Journal of Physics A: Mathematical and Theoretical |
container_volume |
51 |
container_issue |
35 |
container_start_page |
355201 |
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1809758113135329280 |