Dimers on Riemann surfaces II: conformal invariance and scaling limit
Abstract
Given a bounded Riemann surface of finite topological type, we show the existence of a universal and conformally invariant scaling limit for the Temperleyan cycle-rooted spanning forest on any sequence of graphs which approximate in a reasonable sense (essentially, the invariance principle holds and the walks satisfy a crossing assumption). In combination with the companion paper arxiv:1908.00832, this proves the existence of a universal, conformally invariant scaling limit for the height function of the Temperleyan dimer model on such graphs. Along the way, we describe the relationship between Temperleyan CRSFs and loop measures, and develop tools of independent interest to study the latter using only rough control on the random walk
Keywords
Cite
@article{arxiv.2207.09875,
title = {Dimers on Riemann surfaces II: conformal invariance and scaling limit},
author = {Nathanaël Berestycki and Benoit Laslier and Gourab Ray},
journal= {arXiv preprint arXiv:2207.09875},
year = {2024}
}
Comments
v2: 73 pages. Revised in coordination with arXiv:1908.00832 (of which this article is the second part). This version is the one accepted by Probability and Mathematical Physics