A note on dimers and T-graphs
Probability
2016-10-26 v1 Combinatorics
Abstract
The purpose of this note is to give a succinct summary of some basic properties of T-graphs which arise in the study of the dimer model. We focus in particular on the relation between the dimer model on the heaxgonal lattice with a given slope, and the behaviour of the uniform spanning tree on the associated T-graph. Together with the main result of the companion paper \cite{BLR16}, the results here show Gaussian free field fluctuations for the height function in some dimer models.
Cite
@article{arxiv.1610.07994,
title = {A note on dimers and T-graphs},
author = {Nathanaël Berestycki and Benoit Laslier and Gourab Ray},
journal= {arXiv preprint arXiv:1610.07994},
year = {2016}
}