Upcoming events

Abstract: The Discrete Gaussian Free Field (DGFF) serves as a canonical model for random interfaces in statistical mechanics. When conditioned to stay non-negative on a domain—an event known as the "hard wall" constraint—the field undergoes entropic repulsion, lifting away from the wall to accommodate its fluctuations. The study of this phenomenon in two dimensions was pioneered by Bolthausen, Deuschel, and Giacomin (2001), who established the leading-order asymptotics for the probability of the hard wall event. In this talk, I will present two major recent advancements that significantly refine our understanding of this problem: The Binary Tree (Fels, Hartung, Louidor 2024): We first discuss the case of the DGFF on the binary tree, where the hierarchical structure permits a complete derivation of the conditioned field's behavior. We will show that the hard wall constraint leads to a repulsion profile that makes the conditioned law asymptotically mutually singular with respect to the unconditioned law. The 2D Plane (Fels, Louidor, Wu 2026): Turning to the Euclidean lattice $\mathbb{Z}^2$, I will present very recent work that improves upon the classical BDG result by capturing the subleading order of the probability asymptotics. The analysis relies on a novel orthogonal decomposition of the field into a "constant" component and a conditioned remainder, handled via multi-scale analysis and double-exponential tail bounds.