Probability and Mathematical Physics Seminar

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Large deviations for the 3D dimer model

Speaker: Catherine Wolfram, MIT

Location: Warren Weaver Hall 1302

Date: Friday, March 24, 2023, 11:10 a.m.

Notes:

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 our work, we rely on a smaller set of tools including Hall’s matching theorem and a double dimer swapping operation. In this talk, I will explain how to formulate the large deviations principle in 3D, show simulations, give some of the key ideas of our proofs. Time permitting, I will briefly describe a (seemingly simple) open problem which highlights one of the ways that three dimensions is different from two.