Speaker Asaf Nachmias
Host Yuval Peres
Date recorded 30 June 2011
Consider percolation on the Hamming cube 0,1n at the critical probability pc (at which the expected cluster size is 2n/3). It is known that if p=pc(1+O(2-n/3), then the largest component is of size roughly 22n/3 with high probability and that this quantity is non-concentrated. We show that for any sequence eps(n) such that eps(n)2-n/3 and eps(n)=o(1) percolation at pc(1+eps(n)) yields a largest cluster of size (2+o(1))eps(n)2n.
This result settles a conjecture of Borgs, Chayes, van der Hofstad, Slade and Spencer.
Joint work with Remco van der Hofstad.
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