Work

The Tutte embedding of tree-weighted planar maps converges to Liouville quantum gravity

Year: 2026

Type: preprint

Abstract: Suppose $M$ is a planar map with a macroscopic boundary decorated by a spanning tree $T$, such that $(M,T)$ has been sampled from the critical Boltzman measure. We show that $M$ converges to a Liouville quantum gravity disk with parameter $γ=\sqrt{2}$ under the Tutte embedding as the length of the boundary of $M$ goes to infinity. Furthermore, conditioned on $(M,T)$, the simple random walk on $M$ converges to a planar Brownian motion modulo reparametrization of time.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.10501

Author: Holden, Nina

Institutions: Courant Institute of Mathematical Sciences, New York University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7220971231

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