The half plane UIPT is recurrent
Probability Theory and Related Fields
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Angel, O., & Ray, G. (2017). The half plane UIPT is recurrent. Probability Theory and Related Fields https://doi.org/10.1007/s00440-017-0767-z
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).
OA was partly supported by NSERC, the Isaac Newton Institute and the Simons Foundation. GR was supported by the Engineering and Physical Sciences Research Council Under Grant EP/103372X/1.
External DOI: https://doi.org/10.1007/s00440-017-0767-z
This record's URL: https://www.repository.cam.ac.uk/handle/1810/264121