TL;DR
This paper proves that the half plane uniform infinite planar triangulation (UIPT) is recurrent by constructing a full plane extension and applying circle packing methods to establish recurrence.
Contribution
It introduces a novel full plane extension of the half plane UIPT based on a layered decomposition, advancing understanding of recurrence in infinite random planar maps.
Findings
Half plane UIPT is recurrent.
Constructed a new full plane extension of the half plane UIPT.
Extended circle packing methods to prove recurrence.
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).
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