The scaling limit of critical hypercube percolation
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.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Theoretical and Computational Physics
Complex Network Analysis Techniques
Publication details
- Journal / source
- Journal of the European Mathematical Society
- Publisher
- European Mathematical Society - EMS - Publishing House GmbH
- Publication date
- 28 July 2026
- Language
- EN