Grove Arctic Curves from Periodic Cluster Modular Transformations
Abstract Groves are spanning forests of a finite region of the triangular lattice that are in bijection with Laurent monomials that arise in solutions of the cube recurrence. We introduce a large class of probability measures on groves for which we can compute exact generating functions for edge pro...
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Online Access: | http://dx.doi.org/10.1093/imrn/rnz367 http://academic.oup.com/imrn/article-pdf/2021/20/15301/40740074/rnz367.pdf |
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croxfordunivpr:10.1093/imrn/rnz367 2023-05-15T14:40:49+02:00 Grove Arctic Curves from Periodic Cluster Modular Transformations George, Terrence 2020 http://dx.doi.org/10.1093/imrn/rnz367 http://academic.oup.com/imrn/article-pdf/2021/20/15301/40740074/rnz367.pdf en eng Oxford University Press (OUP) https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model International Mathematics Research Notices volume 2021, issue 20, page 15301-15336 ISSN 1073-7928 1687-0247 General Mathematics journal-article 2020 croxfordunivpr https://doi.org/10.1093/imrn/rnz367 2022-04-15T06:34:49Z Abstract Groves are spanning forests of a finite region of the triangular lattice that are in bijection with Laurent monomials that arise in solutions of the cube recurrence. We introduce a large class of probability measures on groves for which we can compute exact generating functions for edge probabilities. Using the machinery of asymptotics of multivariate generating functions, this lets us explicitly compute arctic curves, generalizing the arctic circle theorem of Petersen and Speyer. Our class of probability measures is sufficiently general that the limit shapes exhibit all solid and gaseous phases expected from the classification of ergodic Gibbs measures in the resistor network model. Article in Journal/Newspaper Arctic Oxford University Press (via Crossref) Arctic Petersen ENVELOPE(-101.250,-101.250,-71.917,-71.917) International Mathematics Research Notices |
institution |
Open Polar |
collection |
Oxford University Press (via Crossref) |
op_collection_id |
croxfordunivpr |
language |
English |
topic |
General Mathematics |
spellingShingle |
General Mathematics George, Terrence Grove Arctic Curves from Periodic Cluster Modular Transformations |
topic_facet |
General Mathematics |
description |
Abstract Groves are spanning forests of a finite region of the triangular lattice that are in bijection with Laurent monomials that arise in solutions of the cube recurrence. We introduce a large class of probability measures on groves for which we can compute exact generating functions for edge probabilities. Using the machinery of asymptotics of multivariate generating functions, this lets us explicitly compute arctic curves, generalizing the arctic circle theorem of Petersen and Speyer. Our class of probability measures is sufficiently general that the limit shapes exhibit all solid and gaseous phases expected from the classification of ergodic Gibbs measures in the resistor network model. |
format |
Article in Journal/Newspaper |
author |
George, Terrence |
author_facet |
George, Terrence |
author_sort |
George, Terrence |
title |
Grove Arctic Curves from Periodic Cluster Modular Transformations |
title_short |
Grove Arctic Curves from Periodic Cluster Modular Transformations |
title_full |
Grove Arctic Curves from Periodic Cluster Modular Transformations |
title_fullStr |
Grove Arctic Curves from Periodic Cluster Modular Transformations |
title_full_unstemmed |
Grove Arctic Curves from Periodic Cluster Modular Transformations |
title_sort |
grove arctic curves from periodic cluster modular transformations |
publisher |
Oxford University Press (OUP) |
publishDate |
2020 |
url |
http://dx.doi.org/10.1093/imrn/rnz367 http://academic.oup.com/imrn/article-pdf/2021/20/15301/40740074/rnz367.pdf |
long_lat |
ENVELOPE(-101.250,-101.250,-71.917,-71.917) |
geographic |
Arctic Petersen |
geographic_facet |
Arctic Petersen |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
International Mathematics Research Notices volume 2021, issue 20, page 15301-15336 ISSN 1073-7928 1687-0247 |
op_rights |
https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model |
op_doi |
https://doi.org/10.1093/imrn/rnz367 |
container_title |
International Mathematics Research Notices |
_version_ |
1766312681423241216 |