AN ARCTIC CIRCLE THEOREM FOR GROVES
Abstract. In earlier work, Jockusch, Propp, and Shor proved a theorem describing the limiting shape of the boundary between the uniformly tiled corners of a random tiling of an Aztec diamond and the more unpredictable ‘temperate zone ’ in the interior of the region. The so-called arctic circle theor...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.92.5140 2023-05-15T14:42:43+02:00 AN ARCTIC CIRCLE THEOREM FOR GROVES T. Kyle Petersen David Speyer The Pennsylvania State University CiteSeerX Archives application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.5140 http://people.brandeis.edu/~tkpeters/Articles/GroveArticle/GROVEfullv4.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.5140 http://people.brandeis.edu/~tkpeters/Articles/GroveArticle/GROVEfullv4.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://people.brandeis.edu/~tkpeters/Articles/GroveArticle/GROVEfullv4.pdf text ftciteseerx 2016-01-08T19:50:48Z Abstract. In earlier work, Jockusch, Propp, and Shor proved a theorem describing the limiting shape of the boundary between the uniformly tiled corners of a random tiling of an Aztec diamond and the more unpredictable ‘temperate zone ’ in the interior of the region. The so-called arctic circle theorem made precise a phenomenon observed in random tilings of large Aztec diamonds. Here we examine a related combinatorial model called groves. Created by Carroll and Speyer as combinatorial interpretations for Laurent polynomials given by the cube recurrence, groves have observable frozen regions which we describe precisely via asymptotic analysis of a generating function. Our approach also provides another way to prove the arctic circle theorem for Aztec diamonds. 1. Text Arctic Unknown Arctic Carroll ENVELOPE(-81.183,-81.183,50.800,50.800) |
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Unknown |
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ftciteseerx |
language |
English |
description |
Abstract. In earlier work, Jockusch, Propp, and Shor proved a theorem describing the limiting shape of the boundary between the uniformly tiled corners of a random tiling of an Aztec diamond and the more unpredictable ‘temperate zone ’ in the interior of the region. The so-called arctic circle theorem made precise a phenomenon observed in random tilings of large Aztec diamonds. Here we examine a related combinatorial model called groves. Created by Carroll and Speyer as combinatorial interpretations for Laurent polynomials given by the cube recurrence, groves have observable frozen regions which we describe precisely via asymptotic analysis of a generating function. Our approach also provides another way to prove the arctic circle theorem for Aztec diamonds. 1. |
author2 |
The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
T. Kyle Petersen David Speyer |
spellingShingle |
T. Kyle Petersen David Speyer AN ARCTIC CIRCLE THEOREM FOR GROVES |
author_facet |
T. Kyle Petersen David Speyer |
author_sort |
T. Kyle |
title |
AN ARCTIC CIRCLE THEOREM FOR GROVES |
title_short |
AN ARCTIC CIRCLE THEOREM FOR GROVES |
title_full |
AN ARCTIC CIRCLE THEOREM FOR GROVES |
title_fullStr |
AN ARCTIC CIRCLE THEOREM FOR GROVES |
title_full_unstemmed |
AN ARCTIC CIRCLE THEOREM FOR GROVES |
title_sort |
arctic circle theorem for groves |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.5140 http://people.brandeis.edu/~tkpeters/Articles/GroveArticle/GROVEfullv4.pdf |
long_lat |
ENVELOPE(-81.183,-81.183,50.800,50.800) |
geographic |
Arctic Carroll |
geographic_facet |
Arctic Carroll |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
http://people.brandeis.edu/~tkpeters/Articles/GroveArticle/GROVEfullv4.pdf |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.5140 http://people.brandeis.edu/~tkpeters/Articles/GroveArticle/GROVEfullv4.pdf |
op_rights |
Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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1766314445035798528 |