29 citations · 82 across the 20 of their papers we have counts for
5 papers · 1 filter
Hyperbolic and Parabolic Unimodular Random Maps
Omer Angel, Tom Hutchcroft, Asaf Nachmias +1
We show that for infinite planar unimodular random rooted maps, many global geometric and probabilistic properties are equivalent, and are determined by a natural, local notion of…
A note on dimers and T-graphs
Nathanaël Berestycki, Benoit Laslier, Gourab Ray
The purpose of this note is to give a succinct summary of some basic properties of T-graphs which arise in the study of the dimer model. We focus in particular on the relation betw…
Classification of scaling limits of uniform quadrangulations with a boundary
Erich Baur, Grégory Miermont, Gourab Ray
We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundar…
Dimers and Imaginary geometry
Nathanaël Berestycki, Benoit Laslier, Gourab Ray
We present a general result which shows that the winding of the branches in a uniform spanning tree on a planar graph converge in the limit of fine mesh size to a Gaussian free fie…
The half plane UIPT is recurrent
Omer Angel, Gourab Ray
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 exten…