A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points
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 positiv...
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ftdatacite:10.48550/arxiv.1810.07936 2023-05-15T14:39:27+02:00 A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points Di Francesco, Philippe Guitter, Emmanuel 2018 https://dx.doi.org/10.48550/arxiv.1810.07936 https://arxiv.org/abs/1810.07936 unknown arXiv https://dx.doi.org/10.1088/1751-8121/ab03ff 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 2018 ftdatacite https://doi.org/10.48550/arxiv.1810.07936 https://doi.org/10.1088/1751-8121/ab03ff 2022-04-01T08:47:12Z 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. : 48 pages, 21 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 Guitter, Emmanuel A tangent method derivation of the arctic curve for q-weighted paths with arbitrary starting points |
topic_facet |
Mathematical Physics math-ph Statistical Mechanics cond-mat.stat-mech Combinatorics math.CO FOS Physical sciences FOS Mathematics |
description |
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. : 48 pages, 21 figures |
format |
Text |
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 |
arXiv |
publishDate |
2018 |
url |
https://dx.doi.org/10.48550/arxiv.1810.07936 https://arxiv.org/abs/1810.07936 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_relation |
https://dx.doi.org/10.1088/1751-8121/ab03ff |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1810.07936 https://doi.org/10.1088/1751-8121/ab03ff |
_version_ |
1766311398193758208 |