Publications (35)
Random walks on stochastic hyperbolic half planar triangulations
Omer Angel, Asaf Nachmias, Gourab Ray
We study the simple random walk on stochastic hyperbolic half planar triangulations constructed in Angel and Ray [3]. We show that almost surely the walker escapes the boundary of…
Proper 3-colorings of are Bernoulli
Gourab Ray, Yinon Spinka
We consider the unique measure of maximal entropy for proper 3-colorings of , or equivalently, the so-called zero-slope Gibbs measure. Our main result is that this me…
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…
Dimers on Riemann surfaces I: Temperleyan forests
Nathanaël Berestycki, Benoit Laslier, Gourab Ray
This is the first article in a series of two papers in which we study the Temperleyan dimer model on an arbitrary bounded Riemann surface of finite topolgical type. The end goal of…
Oriented Minimum spanning tree looks like the Uniform spanning tree on the complete graph (at least locally)
Swarnadeep Bagchi, Gourab Ray
We prove that the local limit of the minimum spanning arborescence in the complete graph (which is an oriented cousin of the minimum spanning tree in the complete graph) is the sam…
Dimers on Riemann surfaces II: conformal invariance and scaling limit
Nathanaël Berestycki, Benoit Laslier, Gourab Ray
Given a bounded Riemann surface of finite topological type, we show the existence of a universal and conformally invariant scaling limit for the Temperleyan cycle-rooted spanni…