@article{ccf9563ff9f94fdeb2eb6934e85e952c,
title = "Hypercube percolation",
abstract = "We study bond percolation on the Hamming hypercube f0; 1gm around the critical probability pc. It is known that if p D pc.1 C O.2-m=3//, then with high probability the largest connected component Here we show that for any sequence {"}.m/such that {"}.m/D o.1/but ϵ.m/percolation on the hypercube at pc.1 C ϵm//has with high probability, where C2 is the second largest component. This resolves a conjecture of Borgs, Chayes, the first author, Slade and Spencer [18].",
keywords = "Birth of the giant component, Critical behavior, Hypercube, Mean-field results, Mixing time, Non-backtracking random walk, Percolation, Scaling window",
author = "{Van Der Hofstad}, Remco and Asaf Nachmias",
note = "Publisher Copyright: {\textcopyright} 2017 European Mathematical Society.",
year = "2017",
doi = "10.4171/JEMS/679",
language = "אנגלית",
volume = "19",
pages = "725--814",
journal = "Journal of the European Mathematical Society",
issn = "1435-9855",
publisher = "European Mathematical Society Publishing House",
number = "3",
}