Gourab Ray

We examine the behavior of a function sampled from the invariant measure asso- ciated to the focusing discrete Non Linear Schrodinger equation, defined on a discrete torus of dimension d≥3, and nonlinearity parameter p > 4, in the infinite volume...

In this article we study the double dimer model on hyperbolic Temper- leyan graphs via circle packings. We prove that on such graphs, the weak limit of the dimer model exists if and only if the removed black vertex from the boundary of an exhaustion...

Double dimers are superimposition of two perfect matchings. Such superimpositions can be decomposed into disjoint simple loops. The question we address is: as the graphs become large, in a 'typical' double dimer sample, do some of the loops diverge...

I will talk about the `minimal spanning arborescence', a directed version of the Minimal spanning tree. I will explain how this naturally leads to a new type of stochastic process which we call `loop contracting random walk'. I will show how this can...

We prove that a well-known graphical expansion of the Ising model, known as the Loop O(1) model, is a factor of i.i.d. on unimodular random rooted graphs under various boundary conditions and in the presence of a non-negative external field. As an...

A spanning tree is a connected subgraph of a graph with no cycles. I will explain some well-known connection between such collection of trees and some Poissonian collection of loops, and a magical algorithm (known as Wilson's alorithm) to sample such...

Take an Ising model with very low temperature. What is the largest p such that the Ising model dominates Bernoulli percolation with parameter p ? We will show that the answer to this question depends drastically on the geometry of the graph. We also...

Planar maps are embeddings of graphs on compact orientable surfaces. We shall consider a special class of maps: triangulations with an infinite simple boundary. We shall consider measures supported on this space satisfying two natural properties...

Uniform infinite maps arise as local limits of uniformly chosen finite maps. Recently there has been keen interest in creating hyperbolic analogues of the uniform infinite planar maps. It is conjectured that uniformly distributed maps on surfaces...

We characterize the GFF as the only random distribution which is conformally invariant and satisfies a domain Markov property. Joint work with Nathanael Berestycki and Ellen Powell.