Perfectly matched perspectives on statistical mechanics, combinatorics and geometry / Perspectives couplées sur la mécanique statistique, la combinatoire et la géométrie

Collection Perfectly matched perspectives on statistical mechanics, combinatorics and geometry / Perspectives couplées sur la mécanique statistique, la combinatoire et la géométrie

Organizer(s) Boutillier, Cédric ; Chhita, Sunil ; George, Terrence ; Li, Zhongyang ; Tilière, Béatrice de

Date(s) 16/06/2025 - 20/06/2025

linked URL https://conferences.cirm-math.fr/3178.html

00:00:00 / 00:00:00

3 5

The multinomial dimer model

By Catherine Wolfram

An $N$ dimer cover of a graph is a collection of edges such that every vertex is contained in exactly $N$ edges of the collection. The multinomial dimer model studies a family of natural but non-uniform measures on $N$ dimer covers. In the large $N$ limit, this model turns out to be exactly solvable in a strong sense, in any dimension $N$. In this talk, I will define the model, and discuss its properties on subgraphs of lattices in the iterated limit as the multiplicity $N$ and then the size of the graph go to infinity, analogous to the scaling limit question for 2D standard dimers addressed by Cohn, Kenyon, and Propp. In this setting we can explicitly compute limit shapes in some examples, in particular for the Aztec diamond and a 3D analog called the Aztec cuboid. I will also discuss the surrounding theory, including explicit formulas for the free energy, large deviations, EulerLagrange equations, gauge functions, and regularity properties of limit shapes.This is joint work with Rick Kenyon.

Information about the video

Date of recording 16/06/2025
Date of publication 03/07/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20365303
Cite this video Wolfram, Catherine (16/06/2025). The multinomial dimer model. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20365303
URL https://dx.doi.org/10.24350/CIRM.V.20365303

Domain(s)

Bibliography

KENYON, Richard et WOLFRAM, Catherine. The multinomial dimer model. arXiv preprint arXiv:2506.12171, 2025. - https://doi.org/10.48550/arXiv.2506.12171

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