The half plane UIPT is recurrent

We prove that the half plane version of the uniform infinite planar triangulation (UIPT) is recurrent. The key ingredients of the proof are a construction of a new full plane extension of the half plane UIPT, based on a natural decomposition of the half plane UIPT into independent layers, and an ext...

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Detalles Bibliográficos
Autores principales: Angel, Omer, Ray, Gourab
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566220/
https://www.ncbi.nlm.nih.gov/pubmed/31258233
http://dx.doi.org/10.1007/s00440-017-0767-z
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author Angel, Omer
Ray, Gourab
author_facet Angel, Omer
Ray, Gourab
author_sort Angel, Omer
collection PubMed
description We prove that the half plane version of the uniform infinite planar triangulation (UIPT) is recurrent. The key ingredients of the proof are a construction of a new full plane extension of the half plane UIPT, based on a natural decomposition of the half plane UIPT into independent layers, and an extension of previous methods for proving recurrence of weak local limits (while still using circle packings).
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spelling pubmed-65662202019-06-28 The half plane UIPT is recurrent Angel, Omer Ray, Gourab Probab Theory Relat Fields Article We prove that the half plane version of the uniform infinite planar triangulation (UIPT) is recurrent. The key ingredients of the proof are a construction of a new full plane extension of the half plane UIPT, based on a natural decomposition of the half plane UIPT into independent layers, and an extension of previous methods for proving recurrence of weak local limits (while still using circle packings). Springer Berlin Heidelberg 2017-03-07 2018 /pmc/articles/PMC6566220/ /pubmed/31258233 http://dx.doi.org/10.1007/s00440-017-0767-z Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Angel, Omer
Ray, Gourab
The half plane UIPT is recurrent
title The half plane UIPT is recurrent
title_full The half plane UIPT is recurrent
title_fullStr The half plane UIPT is recurrent
title_full_unstemmed The half plane UIPT is recurrent
title_short The half plane UIPT is recurrent
title_sort half plane uipt is recurrent
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566220/
https://www.ncbi.nlm.nih.gov/pubmed/31258233
http://dx.doi.org/10.1007/s00440-017-0767-z
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