Arctic Curves in path models from the Tangent Method

Recently, Colomo and Sportiello introduced a powerful method, known as the \emph{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 dom...

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Main Authors: Di Francesco, Philippe, Lapa, Matthew F.
Format: Text
Language:unknown
Published: arXiv 2017
Subjects:
Mathematical Physics math-ph
Statistical Mechanics cond-mat.stat-mech
Combinatorics math.CO
FOS Physical sciences
FOS Mathematics
Arctic
Online Access:https://dx.doi.org/10.48550/arxiv.1711.03182
https://arxiv.org/abs/1711.03182
id ftdatacite:10.48550/arxiv.1711.03182
record_format openpolar
spelling ftdatacite:10.48550/arxiv.1711.03182 2023-05-15T14:33:50+02:00 Arctic Curves in path models from the Tangent Method Di Francesco, Philippe Lapa, Matthew F. 2017 https://dx.doi.org/10.48550/arxiv.1711.03182 https://arxiv.org/abs/1711.03182 unknown arXiv https://dx.doi.org/10.1088/1751-8121/aab3c0 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Mathematical Physics math-ph Statistical Mechanics cond-mat.stat-mech Combinatorics math.CO FOS Physical sciences FOS Mathematics article-journal Article ScholarlyArticle Text 2017 ftdatacite https://doi.org/10.48550/arxiv.1711.03182 https://doi.org/10.1088/1751-8121/aab3c0 2022-04-01T10:11:52Z Recently, Colomo and Sportiello introduced a powerful method, known as the \emph{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. : 63 pages, 13 figures Text Arctic DataCite Metadata Store (German National Library of Science and Technology) Arctic
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Mathematical Physics math-ph
Statistical Mechanics cond-mat.stat-mech
Combinatorics math.CO
FOS Physical sciences
FOS Mathematics
spellingShingle Mathematical Physics math-ph
Statistical Mechanics cond-mat.stat-mech
Combinatorics math.CO
FOS Physical sciences
FOS Mathematics
Di Francesco, Philippe
Lapa, Matthew F.
Arctic Curves in path models from the Tangent Method
topic_facet Mathematical Physics math-ph
Statistical Mechanics cond-mat.stat-mech
Combinatorics math.CO
FOS Physical sciences
FOS Mathematics
description Recently, Colomo and Sportiello introduced a powerful method, known as the \emph{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. : 63 pages, 13 figures
format Text
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 arXiv
publishDate 2017
url https://dx.doi.org/10.48550/arxiv.1711.03182
https://arxiv.org/abs/1711.03182
geographic Arctic
geographic_facet Arctic
genre Arctic
genre_facet Arctic
op_relation https://dx.doi.org/10.1088/1751-8121/aab3c0
op_rights arXiv.org perpetual, non-exclusive license
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
op_doi https://doi.org/10.48550/arxiv.1711.03182
https://doi.org/10.1088/1751-8121/aab3c0
_version_ 1766307016767176704

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