skip to main content
Caltech

LA Probability Forum

Thursday, May 25, 2023
6:00pm to 7:00pm
Add to Cal
Large deviations for the 3D dimer model
Catherine Wolfram, Department of Mathematics, MIT,

UCLA, talks in Math Sciences Room 6627

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 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. Time permitting, I will also describe results and problems that illustrate some of the ways that three dimensions is qualitatively different from two.

For more information, please contact Math Dept by phone at 626-395-4335 or by email at [email protected].