Schnyder woods, \(\mathrm{SLE}_{16}\), and Liouville quantum gravity
type: Item
instance of: scholarly article
title: Schnyder woods, \(\mathrm{SLE}_{16}\), and Liouville quantum gravity
zbMATH Open document ID: 1543.60097
author: Yiting Li
author: Xin Sun
author: Samuel S. Watson
published in: Transactions of the American Mathematical Society
publication date: 2024-07-04T00:00:00Z
review text: The authors consider a 3-spanning-tree decomposition of a simple triangulation, known as the Schnyder wood. In the framework of mating of trees, a uniformly sampled Schnyder-wood-decorated triangulation can produce a triple of random walks. The authors show that these three walks converge in the scaling limit to three Brownian motions produced in the mating-of-trees framework by Liouville quantum gravity (LQG) with parameter \(1,\) decorated with a triple of SLE16's curves. These three SLE16's curves are coupled such that the angle difference between them is \(\frac{2\pi}{3}\) in imaginary geometry. \N\NThe convergence result provides a description of the continuum limit of Schnyder's embedding algorithm via LQG and SLE.
reviewed by: Pavel Stoynov
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60D05
zbMATH DE Number: 7876026
zbMATH Keywords: Schnyder wood
zbMATH Keywords: Schramm-Loewner evolution (SLE)
zbMATH Keywords: Liouville quantum gravity (LQG)
MaRDI profile type: Publication
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DOI: 10.1090/TRAN/8887
description: scientific article; zbMATH DE number 7876026