Date of Award
Spring 2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Kenyon, Richard
Abstract
In this thesis we study several generalizations of the dimer model to higher rank geometric settings.The dimer models, first studied as a toy model in statistical mechanics, exhibit beautiful mathematical structures. It can be exactly enumerated and its probabilistic properties can be studied algebraically. It is also related to geometry and topology. Many versions and generalizations of the dimer model have been studied. Some examples are double dimer models on surfaces. We generalize double dimer models to $n$-dimer models and prove many classical results still hold. Boundaried double dimer models have been extensively studied on the disk. We generalize such results to the annulus. Finally, we study boundaried triple dimer models on the disk and explicitly compute probabilities of triple dimer models on the upper half plane in the scaling limit.
Recommended Citation
Shi, Haolin, "Dimer Models and Local Systems" (2024). Yale Graduate School of Arts and Sciences Dissertations. 1339.
https://elischolar.library.yale.edu/gsas_dissertations/1339
