The scaling limit of critical hypercube percolation
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.
Authors
- Arthur Blanc-Renaudie (ORCID: https://orcid.org/0000-0002-8428-448X)
- Asaf Nachmias (ORCID: https://orcid.org/0000-0002-4852-5645)
- Nicolas Broutin
Institutions
- Tel Aviv University (IL)
- Sorbonne Université (FR)
- Université de Rouen Normandie (FR)
Publication Details
- Journal
- Journal of the European Mathematical Society
- Published
- 2026-07-28
- DOI
- https://doi.org/10.4171/jems/1805
- Citations
- 1
- Primary Topic
- Stochastic processes and statistical mechanics
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Israel Science Foundation
- Tel Aviv University
- Division of Mathematical Sciences