The half plane UIPT is recurrent
Probability
2016-01-05 v1
Abstract
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 (still using circle packings).
Cite
@article{arxiv.1601.00410,
title = {The half plane UIPT is recurrent},
author = {Omer Angel and Gourab Ray},
journal= {arXiv preprint arXiv:1601.00410},
year = {2016}
}