Conformal invariance of dimer heights on isoradial double graphs
Probability
2020-05-12 v2
Abstract
An isoradial graph is a planar graph in which each face is inscribable into a circle of common radius. We study the 2-dimensional perfect matchings on a bipartite isoradial graph, obtained from the union of an isoradial graph and its interior dual graph. Using the isoradial graph to approximate a simply-connected domain bounded by a simple closed curve, by letting the mesh size go to zero, we prove that in the scaling limit, the distribution of height is conformally invariant and converges to a Gaussian free field.
Keywords
Cite
@article{arxiv.1309.0151,
title = {Conformal invariance of dimer heights on isoradial double graphs},
author = {Zhongyang Li},
journal= {arXiv preprint arXiv:1309.0151},
year = {2020}
}