Gourab Ray

My research interest mainly lies in the intersection of probability theory, geometry and mathematical physics. Broadly, I look for large scale patterns in problems related to certain stochastic models with motivation coming from mathematical physics in most cases. A basic example would be the behaviour of a magnet: when we heat up a magnet, it gets demagnetized. Or for example, an ice crystal melts when heated. Or, for example if we have gas particles moving around randomly in space, what is the principle that governs their movement and predicts their behaviour in advance?

It turns out the mathematics behind these transformations are very similar, and all these problems come from a subject called statistical physics. I am mostly interested problems of these flavour.

To be more technical, I am interested in various topics which include random planar maps, random walks, lattice spin models, dimer model, Gaussian free field and its properties and Liouville quantum gravity. More recently I have been interested in establishing universal Gaussian free field like behaviour on dimer models on a large class of graphs and surfaces.

Interests

• Probability theory
• Statistical physics
• Stochastic processes

Courses

• Fall 2024: MATH 236: Introduction to Real Analysis 
• Spring 2025: MATH 236: Introduction to Real Analysis  MATH 451: Probability  MATH 555: Topics in Probability 
• Summer 2025:

Selected Publications

• Unimodular hyperbolic triangulations: circle packing and random walk. (with Omer Angel, Tom Hutchcroft and Asaf Nachmias). In Inventiones Mathematicae.
• Classification of half planar maps (with Omer Angel) In Ann. Probab. Volume 43, Number 3 (2015), 1315-1349.
• Dimers and imaginary geometry (with Nathanael Berestycki and Benoit Laslier). Ann. Probab. In Press.
• Hyperbolic and parabolic unimodular random maps (with Omer Angel, Tom Hutchcroft and Asaf Nachmias). GAFA, 06, 229-268, 2018
• A characterization of the Gaussian free field. (with N. Berestycki and B. Laslier). PTRF. In press.