Tangent method for the arctic curve arising from freezing boundaries
In the paper [1], the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for portions of arctic curve in terms of an arbitrary piecewise differentiable funct...
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ftunistlouisbrus:oai:dial.uclouvain.be:boreal:212642 2023-05-15T14:35:10+02:00 Tangent method for the arctic curve arising from freezing boundaries Debin, Bryan Ruelle, Philippe UCL - SST/IRMP - Institut de recherche en mathématique et physique 2018 http://hdl.handle.net/2078.1/212642 eng eng boreal:212642 http://hdl.handle.net/2078.1/212642 info:eu-repo/semantics/workingPaper 2018 ftunistlouisbrus 2019-07-03T22:17:34Z In the paper [1], the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for portions of arctic curve in terms of an arbitrary piecewise differentiable function that describes the defect distribution. When this distribution presents "freezing" intervals, other portions of arctic curve appear and typically have a cusp. These freezing boundaries can be of two types, respectively with maximal or minimal density of defects. Our purpose here is to extend the tangent method derivation of [1] to include these portions, hence providing the proof of the conjectures made in [1]. Report Arctic DIAL@USL-B (Université Saint-Louis, Bruxelles) Arctic |
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Open Polar |
collection |
DIAL@USL-B (Université Saint-Louis, Bruxelles) |
op_collection_id |
ftunistlouisbrus |
language |
English |
description |
In the paper [1], the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for portions of arctic curve in terms of an arbitrary piecewise differentiable function that describes the defect distribution. When this distribution presents "freezing" intervals, other portions of arctic curve appear and typically have a cusp. These freezing boundaries can be of two types, respectively with maximal or minimal density of defects. Our purpose here is to extend the tangent method derivation of [1] to include these portions, hence providing the proof of the conjectures made in [1]. |
author2 |
UCL - SST/IRMP - Institut de recherche en mathématique et physique |
format |
Report |
author |
Debin, Bryan Ruelle, Philippe |
spellingShingle |
Debin, Bryan Ruelle, Philippe Tangent method for the arctic curve arising from freezing boundaries |
author_facet |
Debin, Bryan Ruelle, Philippe |
author_sort |
Debin, Bryan |
title |
Tangent method for the arctic curve arising from freezing boundaries |
title_short |
Tangent method for the arctic curve arising from freezing boundaries |
title_full |
Tangent method for the arctic curve arising from freezing boundaries |
title_fullStr |
Tangent method for the arctic curve arising from freezing boundaries |
title_full_unstemmed |
Tangent method for the arctic curve arising from freezing boundaries |
title_sort |
tangent method for the arctic curve arising from freezing boundaries |
publishDate |
2018 |
url |
http://hdl.handle.net/2078.1/212642 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_relation |
boreal:212642 http://hdl.handle.net/2078.1/212642 |
_version_ |
1766308051741048832 |