Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains ...
In this paper we study uniformly random lozenge tilings of strip domains. Under the assumption that the limiting arctic boundary has at most one cusp, we prove a nearly optimal concentration estimate for the tiling height functions and arctic boundaries on such domains: with overwhelming probability...
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Online Access: | https://dx.doi.org/10.48550/arxiv.2108.12872 https://arxiv.org/abs/2108.12872 |
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ftdatacite:10.48550/arxiv.2108.12872 2023-06-11T04:08:34+02:00 Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains ... Huang, Jiaoyang 2021 https://dx.doi.org/10.48550/arxiv.2108.12872 https://arxiv.org/abs/2108.12872 unknown arXiv Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 Probability math.PR FOS Mathematics 60F05, 60K35, 82B20 CreativeWork Article article Preprint 2021 ftdatacite https://doi.org/10.48550/arxiv.2108.12872 2023-05-02T10:50:41Z In this paper we study uniformly random lozenge tilings of strip domains. Under the assumption that the limiting arctic boundary has at most one cusp, we prove a nearly optimal concentration estimate for the tiling height functions and arctic boundaries on such domains: with overwhelming probability the tiling height function is within $n^δ$ of its limit shape, and the tiling arctic boundary is within $n^{1/3+δ}$ to its limit shape, for arbitrarily small $δ>0$. This concentration result will be used in [AH21] to prove that the edge statistics of simply-connected polygonal domains, subject to a technical assumption on their limit shape, converge to the Airy line ensemble. ... : 90 pages, 21 figures, this is Part I of a two-paper series ... Report Arctic DataCite Metadata Store (German National Library of Science and Technology) Arctic |
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DataCite Metadata Store (German National Library of Science and Technology) |
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language |
unknown |
topic |
Probability math.PR FOS Mathematics 60F05, 60K35, 82B20 |
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Probability math.PR FOS Mathematics 60F05, 60K35, 82B20 Huang, Jiaoyang Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains ... |
topic_facet |
Probability math.PR FOS Mathematics 60F05, 60K35, 82B20 |
description |
In this paper we study uniformly random lozenge tilings of strip domains. Under the assumption that the limiting arctic boundary has at most one cusp, we prove a nearly optimal concentration estimate for the tiling height functions and arctic boundaries on such domains: with overwhelming probability the tiling height function is within $n^δ$ of its limit shape, and the tiling arctic boundary is within $n^{1/3+δ}$ to its limit shape, for arbitrarily small $δ>0$. This concentration result will be used in [AH21] to prove that the edge statistics of simply-connected polygonal domains, subject to a technical assumption on their limit shape, converge to the Airy line ensemble. ... : 90 pages, 21 figures, this is Part I of a two-paper series ... |
format |
Report |
author |
Huang, Jiaoyang |
author_facet |
Huang, Jiaoyang |
author_sort |
Huang, Jiaoyang |
title |
Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains ... |
title_short |
Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains ... |
title_full |
Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains ... |
title_fullStr |
Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains ... |
title_full_unstemmed |
Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains ... |
title_sort |
edge statistics for lozenge tilings of polygons, i: concentration of height function on strip domains ... |
publisher |
arXiv |
publishDate |
2021 |
url |
https://dx.doi.org/10.48550/arxiv.2108.12872 https://arxiv.org/abs/2108.12872 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_rights |
Creative Commons Attribution 4.0 International https://creativecommons.org/licenses/by/4.0/legalcode cc-by-4.0 |
op_doi |
https://doi.org/10.48550/arxiv.2108.12872 |
_version_ |
1768381872752033792 |