2:30–3:30 pm
Eckhart Hall, Room 202 5734 S. University Avenue
Catherine Wolfram, Massachusetts Institute of Technology
“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 random 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. I will explain how to formulate the large deviations principle in 3D, show simulations, try to give some intuition for why three dimensions is different from two, 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.