7 papers · 1 filter
Forests on wired regular trees
Gourab Ray, Ben Xiao
The Arboreal gas model on a finite graph is the Bernoulli bond percolation on conditioned on the event that the sampled subgraph is a forest. In this short note we study th…
Quantitative Russo-Seymour-Welsh for random walk on random graphs and decorrelation of UST
Gourab Ray, Tingzhou Yu
We prove a quantitative Russo-Seymour-Welsh (RSW) type result for random walks on two natural examples of random planar graphs: the supercritical percolation cluster in the square…
A tale of two balloons
Omer Angel, Gourab Ray, Yinon Spinka
From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often…
-moments suffice to characterise the GFF
Nathanaël Berestycki, Ellen Powell, Gourab Ray
We show that there is "no stable free field of index ", in the following sense. It was proved in a previous work by the authors, that subject to a \emph{fourth moment a…
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…
A short proof of the discontinuity of phase transition in the planar random-cluster model with
Gourab Ray, Yinon Spinka
The goal of this paper is to provide a short proof of the discontinuity of phase transition for the random-cluster model on the square lattice with parameter . This result was…