The arctic circle boundary and the Airy process

We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp's conjecture concerning the structure...

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Main Author: Johansson, Kurt
Format: Text
Language:unknown
Published: arXiv 2003
Subjects:
Probability math.PR
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
60K35 Primary 82B20, 15A52. Secondary
Arctic
Online Access:https://dx.doi.org/10.48550/arxiv.math/0306216
https://arxiv.org/abs/math/0306216
id ftdatacite:10.48550/arxiv.math/0306216
record_format openpolar
spelling ftdatacite:10.48550/arxiv.math/0306216 2023-05-15T14:58:26+02:00 The arctic circle boundary and the Airy process Johansson, Kurt 2003 https://dx.doi.org/10.48550/arxiv.math/0306216 https://arxiv.org/abs/math/0306216 unknown arXiv https://dx.doi.org/10.3189/172756405781813708 Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004 http://arxiv.org/licenses/assumed-1991-2003/ Probability math.PR Mathematical Physics math-ph FOS Mathematics FOS Physical sciences 60K35 Primary 82B20, 15A52. Secondary article-journal Article ScholarlyArticle Text 2003 ftdatacite https://doi.org/10.48550/arxiv.math/0306216 https://doi.org/10.3189/172756405781813708 2022-04-01T16:29:12Z We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp's conjecture concerning the structure of the tiling at the center of the Aztec diamond. : Published at http://dx.doi.org/10.1214/009117904000000937 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) 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 Probability math.PR
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
60K35 Primary 82B20, 15A52. Secondary
spellingShingle Probability math.PR
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
60K35 Primary 82B20, 15A52. Secondary
Johansson, Kurt
The arctic circle boundary and the Airy process
topic_facet Probability math.PR
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
60K35 Primary 82B20, 15A52. Secondary
description We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp's conjecture concerning the structure of the tiling at the center of the Aztec diamond. : Published at http://dx.doi.org/10.1214/009117904000000937 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
format Text
author Johansson, Kurt
author_facet Johansson, Kurt
author_sort Johansson, Kurt
title The arctic circle boundary and the Airy process
title_short The arctic circle boundary and the Airy process
title_full The arctic circle boundary and the Airy process
title_fullStr The arctic circle boundary and the Airy process
title_full_unstemmed The arctic circle boundary and the Airy process
title_sort arctic circle boundary and the airy process
publisher arXiv
publishDate 2003
url https://dx.doi.org/10.48550/arxiv.math/0306216
https://arxiv.org/abs/math/0306216
geographic Arctic
geographic_facet Arctic
genre Arctic
genre_facet Arctic
op_relation https://dx.doi.org/10.3189/172756405781813708
op_rights Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004
http://arxiv.org/licenses/assumed-1991-2003/
op_doi https://doi.org/10.48550/arxiv.math/0306216
https://doi.org/10.3189/172756405781813708
_version_ 1766330527871139840

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