The scaling limit of critical hypercube percolation

2024/01/29 by Blanc-Renaudie, Arthur, Broutin, Nicolas, Nachmias, Asaf · 3 citations
#60D05 #60F05 #60K35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2401.16365

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 Erdős-Rényi graphs.

Cited by

• Diameter and mixing time of the giant component in the percolated hypercube
• Geometry of critical discrete structures: percolation on the hierarchical lattice
• Existence and uniqueness of the conformally covariant geodesic metric on non-simple conformal loop ensemble gaskets

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