Work

The scaling limit of critical hypercube percolation

Year: 2026

Type: article

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.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1805

Authors: Arthur Blanc-Renaudie, Nicolas Broutin, Asaf Nachmias

Institutions: Université de Rouen Normandie, Sorbonne Université, Tel Aviv University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Israel Science Foundation, Tel Aviv University, Division of Mathematical Sciences, H2020 European Research Council

Awards: G2004740150, Universality of random planar maps and trees