Grove arctic curves from periodic cluster modular transformations
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 probabilitie...
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ftdatacite:10.48550/arxiv.1711.00790 2023-05-15T14:40:47+02:00 Grove arctic curves from periodic cluster modular transformations George, Terrence 2017 https://dx.doi.org/10.48550/arxiv.1711.00790 https://arxiv.org/abs/1711.00790 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Probability math.PR Combinatorics math.CO FOS Mathematics Preprint Article article CreativeWork 2017 ftdatacite https://doi.org/10.48550/arxiv.1711.00790 2022-04-01T10:28:58Z 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 EGMs in the resistor network model. Report Arctic DataCite Metadata Store (German National Library of Science and Technology) Arctic Petersen ENVELOPE(-101.250,-101.250,-71.917,-71.917) |
institution |
Open Polar |
collection |
DataCite Metadata Store (German National Library of Science and Technology) |
op_collection_id |
ftdatacite |
language |
unknown |
topic |
Probability math.PR Combinatorics math.CO FOS Mathematics |
spellingShingle |
Probability math.PR Combinatorics math.CO FOS Mathematics George, Terrence Grove arctic curves from periodic cluster modular transformations |
topic_facet |
Probability math.PR Combinatorics math.CO FOS Mathematics |
description |
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 EGMs in the resistor network model. |
format |
Report |
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 |
arXiv |
publishDate |
2017 |
url |
https://dx.doi.org/10.48550/arxiv.1711.00790 https://arxiv.org/abs/1711.00790 |
long_lat |
ENVELOPE(-101.250,-101.250,-71.917,-71.917) |
geographic |
Arctic Petersen |
geographic_facet |
Arctic Petersen |
genre |
Arctic |
genre_facet |
Arctic |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1711.00790 |
_version_ |
1766312655980593152 |