Around planar dimer models: Schur processes and integrable statistical mechanics on isoradial graphs
Year: 2016
Type: dissertation
Abstract: The dimer model is a probability measure on perfect matchings (or dimer configurations)on a graph. Dimer models on some subgraphs of the honeycomb and square lattices, whichby duality, correspond to tilings with rhombi and dominos, are directly related to Schurprocesses, probability measures on sequences of interlacing partitions. Via bijectionsand other combinatorial correspondences, other integrable models of two-dimensionalstatistical mechanics can be mapped to planar dimer models: spanning trees, the Isingmodel…This manuscript presents an overview of the results obtained by the author and hiscoauthors on questions around planar dimer models, with a strong emphasis, on onehand, on the relation with Schur processes, and on the other hand, on these models fromstatistical mechanics related to dimers, defined on isoradial graphs, a particular class ofembedded planar graphs with interesting properties.
Source: HAL
Author: Boutillier, Cédric
Institution: Laboratoire de Probabilités et Modèles Aléatoires
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2732765981