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The half plane UIPT is recurrent
(SpringerProbability Theory and Related Fields, 2017-03-07)
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 ...
Critical Exponents on Fortuin-Kasteleyn Weighted Planar Maps
(SpringerCOMMUNICATIONS IN MATHEMATICAL PHYSICS, 2017-10-01)
In this paper we consider random planar maps weighted by the self-dual Fortuin--Kasteleyn model with parameter $q \in (0,4)$. Using a bijection due to Sheffield and a connection to planar Brownian motion in a cone we obtain ...