A tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points
International audience We use a tangent method approach to obtain the arctic curve in a model of non-intersecting lattice paths within the first quadrant, including a $q$-dependent weight associated with the area delimited by the paths. Our model is characterized by an arbitrary sequence of starting...
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ftccsdartic:oai:HAL:cea-02932285v1 2023-05-15T14:34:21+02:00 A tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points Di Francesco, Philippe Guitter, Emmanuel Department of Mathematics, Illinois State University Illinois State University Institut de Physique Théorique - UMR CNRS 3681 (IPHT) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) Université Paris-Saclay ANR-14-CE25-0014,GRAAL,GRaphes et Arbres ALéatoires(2014) 2019-03-15 https://hal-cea.archives-ouvertes.fr/cea-02932285 https://hal-cea.archives-ouvertes.fr/cea-02932285/document https://hal-cea.archives-ouvertes.fr/cea-02932285/file/1810.07936v1.pdf https://doi.org/10.1088/1751-8121/ab03ff en eng HAL CCSD IOP Publishing info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/ab03ff cea-02932285 https://hal-cea.archives-ouvertes.fr/cea-02932285 https://hal-cea.archives-ouvertes.fr/cea-02932285/document https://hal-cea.archives-ouvertes.fr/cea-02932285/file/1810.07936v1.pdf doi:10.1088/1751-8121/ab03ff info:eu-repo/semantics/OpenAccess ISSN: 1751-8113 EISSN: 1751-8121 Journal of Physics A: Mathematical and Theoretical https://hal-cea.archives-ouvertes.fr/cea-02932285 Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2019, 52 (11), pp.115205. ⟨10.1088/1751-8121/ab03ff⟩ non-intersecting lattice paths continuum limit arctic curve [PHYS]Physics [physics] info:eu-repo/semantics/article Journal articles 2019 ftccsdartic https://doi.org/10.1088/1751-8121/ab03ff 2021-12-19T00:57:02Z International audience We use a tangent method approach to obtain the arctic curve in a model of non-intersecting lattice paths within the first quadrant, including a $q$-dependent weight associated with the area delimited by the paths. Our model is characterized by an arbitrary sequence of starting points along the positive horizontal axis, whose distribution involves an arbitrary piecewise differentiable function. We give an explicit expression for the arctic curve in terms of this arbitrary function and of the parameter $q$. A particular emphasis is put on the deformation of the arctic curve upon varying $q$, and on its limiting shapes when $q$ tends to $0$ or infinity. Our analytic results are illustrated by a number of detailed examples. Article in Journal/Newspaper Arctic Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) Arctic Journal of Physics A: Mathematical and Theoretical 52 11 115205 |
institution |
Open Polar |
collection |
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
op_collection_id |
ftccsdartic |
language |
English |
topic |
non-intersecting lattice paths continuum limit arctic curve [PHYS]Physics [physics] |
spellingShingle |
non-intersecting lattice paths continuum limit arctic curve [PHYS]Physics [physics] Di Francesco, Philippe Guitter, Emmanuel A tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points |
topic_facet |
non-intersecting lattice paths continuum limit arctic curve [PHYS]Physics [physics] |
description |
International audience We use a tangent method approach to obtain the arctic curve in a model of non-intersecting lattice paths within the first quadrant, including a $q$-dependent weight associated with the area delimited by the paths. Our model is characterized by an arbitrary sequence of starting points along the positive horizontal axis, whose distribution involves an arbitrary piecewise differentiable function. We give an explicit expression for the arctic curve in terms of this arbitrary function and of the parameter $q$. A particular emphasis is put on the deformation of the arctic curve upon varying $q$, and on its limiting shapes when $q$ tends to $0$ or infinity. Our analytic results are illustrated by a number of detailed examples. |
author2 |
Department of Mathematics, Illinois State University Illinois State University Institut de Physique Théorique - UMR CNRS 3681 (IPHT) Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) Université Paris-Saclay 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 |
A tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points |
title_short |
A tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points |
title_full |
A tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points |
title_fullStr |
A tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points |
title_full_unstemmed |
A tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points |
title_sort |
tangent method derivation of the arctic curve for $q$-weighted paths with arbitrary starting points |
publisher |
HAL CCSD |
publishDate |
2019 |
url |
https://hal-cea.archives-ouvertes.fr/cea-02932285 https://hal-cea.archives-ouvertes.fr/cea-02932285/document https://hal-cea.archives-ouvertes.fr/cea-02932285/file/1810.07936v1.pdf https://doi.org/10.1088/1751-8121/ab03ff |
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://hal-cea.archives-ouvertes.fr/cea-02932285 Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2019, 52 (11), pp.115205. ⟨10.1088/1751-8121/ab03ff⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8121/ab03ff cea-02932285 https://hal-cea.archives-ouvertes.fr/cea-02932285 https://hal-cea.archives-ouvertes.fr/cea-02932285/document https://hal-cea.archives-ouvertes.fr/cea-02932285/file/1810.07936v1.pdf doi:10.1088/1751-8121/ab03ff |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1088/1751-8121/ab03ff |
container_title |
Journal of Physics A: Mathematical and Theoretical |
container_volume |
52 |
container_issue |
11 |
container_start_page |
115205 |
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1766307401108029440 |