Geodesic
Hypercube percolation
Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 725-814.

Voir la notice de l'article provenant de la source EMS Press

We study bond percolation on the Hamming hypercube {0,1}m around the critical probability pc​. It is known that if p=pc​(1+O(2−m/3)), then with high probability the largest connected component C1​ is of size Θ(22m/3). Here we show that for any sequence ε(m) such that ε(m)=o(1) but ε(m)≫2−m/3 percolation on the hypercube at pc​(1+ε(m)) has
DOI : 10.4171/jems/679
Classification : 60-XX, 05-XX, 82-XX
Keywords: Hypercube, percolation, critical behavior, mean-field results, scaling window, birth of the giant component, non-backtracking random walk, mixing time 
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     author = {Remco van der Hofstad and Asaf Nachmias},
     title = {Hypercube percolation},
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     year = {2017},
     doi = {10.4171/jems/679},
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}
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Remco van der Hofstad; Asaf Nachmias. Hypercube percolation. Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 725-814. doi : 10.4171/jems/679. http://geodesic.mathdoc.fr/articles/10.4171/jems/679/

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