The PIMS Postdoctoral Fellow Seminar: Kesav Krishnan

In this talk, I will describe how certain non-linear exponential tilts of the Discrete Gaussian Free Field yield invariant measures for a discretized PDE, the focusing Non Linear Schr\”odinger equation. I will briefly talk about how this tilted measure relates to self-intersections of the random walk on $\mathbb{Z}^{d}$. I will then describe joint work with Partha Dey and Kay Kirkpatrick on how this measure undergoes a phase transition in the thermodynamic limit with general $d\geq 3$ and non-linearity $p$. I will conclude with some new results with Gourab Ray, on the weak convergence of the random field sampled with respect to this measure to the massive discrete Gaussian Free Field.