English

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}
}