Work

The scaling limit of random cubic planar graphs

Year: 2024

Type: article

Abstract: We study the random cubic planar graph with an even number of vertices. We show that the Brownian map arises as Gromov–Hausdorff–Prokhorov scaling limit of as tends to infinity, after rescaling distances by for a specific constant . This is the first time a model of random graphs that are not embedded into the plane is shown to converge to the Brownian map. Our approach features a new method that allows us to relate distances on random graphs to first‐passage percolation distances on their 3‐connected core.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70018

Author: Benedikt Stufler

Institution: TU Wien

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funder: Austrian Science Fund