The scaling limit of random cubic planar graphs

2022/03/14 by Benedikt Stufler, Stufler, Benedikt
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2203.07306

openalex publication_date 2022/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the random simple connected cubic planar graph C_n with an even number n of vertices. We show that the Brownian map arises as Gromov--Hausdorff--Prokhorov scaling limit of C_n as n ∈ 2 \ndN tends to infinity, after rescaling distances by γn^-1/4 for a specific constant γ>0.

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