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arXiv · 2401.16365

The scaling limit of critical hypercube percolation

Arthur Blanc-Renaudie·Nicolas Broutin·Asaf Nachmias
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Abstract

We study the connected components in critical percolation on the Hamming hypercube $\{0,1\}^m$. We show that their sizes rescaled by $2^{-2m/3}$ converge in distribution, and that, considered as metric measure spaces with the graph distance rescaled by $2^{-m/3}$ and the uniform measure, they converge in distribution with respect to the Gromov-Hausdorff-Prokhorov topology. The two corresponding limits are as in critical Erd\H{o}s-R\'enyi graphs.

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Arthur Blanc-Renaudie, Nicolas Broutin, Asaf Nachmias. 2024-01-29. The scaling limit of critical hypercube percolation. https://arxiv.org/abs/2401.16365

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