Large deviations for the 3D dimer model

09/27/2023 3:30 pm - 4:30 pm
Benjamin McKenna Changji Xu Kevin Yang
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Probability Seminar

Speaker: Catherine Wolfram (MIT)

Title: Large deviations for the 3D dimer model

Abstract: A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. In this talk, I will try to give some intuition for why three dimensions is different from two, explain how to formulate the large deviations principle in 3D, show simulations, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments.