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arXiv · 2203.07306

The scaling limit of random cubic planar graphs

Benedikt Stufler
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Abstract

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

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Benedikt Stufler. 2022-03-14. The scaling limit of random cubic planar graphs. https://arxiv.org/abs/2203.07306

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