Geodesic
Hypercube percolation
Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 725-814 Cet article a éte moissonné depuis la source EMS Press

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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 
@article{JEMS_2017_19_3_a2,
     author = {Remco van der Hofstad and Asaf Nachmias},
     title = {Hypercube percolation},
     journal = {Journal of the European Mathematical Society},
     pages = {725--814},
     year = {2017},
     volume = {19},
     number = {3},
     doi = {10.4171/jems/679},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/679/}
}
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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

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