Student Probability Seminar

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On level line fluctuations of SOS surfaces above a wall

Speaker: Yujin H Kim, NYU Courant

Location: Warren Weaver Hall 202

Date: Wednesday, March 27, 2024, 12:30 p.m.

Synopsis:

We introduce the study of interfaces in models of lattice statistical mechanics. Such interfaces are discrete random surfaces, whose fluctuations and scaling limits play a central role in modern probability theory. We discuss interfaces in the 3D Ising model at low-temperature, which will lead us to the (2+1)D solid-on-solid (SOS) model. Of special interest is the behavior of these models "above a hard wall", i.e., the interface conditioned to have non-negative height (think, a crystal or droplet forming on a table). We present both rigorous and conjectural aspects of these models. Based on joint work with Patrizio Caddeo and Eyal Lubetzky.