Publication: Random cubic planar graphs converge to the Brownian sphere
Random cubic planar graphs converge to the Brownian sphere
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Albenque, M., Fusy, É., & Lehéricy, T. (2023). Random cubic planar graphs converge to the Brownian sphere. Electronic Journal of Probability, 28, 1–54. https://doi.org/10.1214/23-ejp912
Abstract
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In this paper, the scaling limit of random connected cubic planar graphs (respectively multigraphs) is shown to be the Brownian sphere.
The proof consists in essentially two main steps. First, thanks to the known decomposition of cubic planar graphs into their 3-connected components, the metric structure of a random cubic planar graph is shown to be well approximated by its unique 3-connected component of linear size, with modified distances.
Then, Whitney's theorem ensures that a 3-connected cubic planar graph is the dual of a simp
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- Albenque, Marie
- Fusy, Éric
- Lehéricy, Thomas
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Albenque, M., Fusy, É., & Lehéricy, T. (2023). Random cubic planar graphs converge to the Brownian sphere. Electronic Journal of Probability, 28, 1–54. https://doi.org/10.1214/23-ejp912
