Speaker Asaf Nachmias
Affiliation University of California - Berkeley
Host Yuval Peres
Date recorded 27 February 2007
Let C1 denote the largest connected component of the critical Erdos-Renyi random graph G(n,1/n). We show that, typically, the diameter of C1 is of order n1/3 and the mixing time of the lazy simple random walk on C1 is of order n. The latter answers a question of Benjamini, Kozma and Wormald.
These results extend to clusters of size n2/3 of p-bond percolation on any d-regular n-vertex graph where such clusters exist, provided that p(d-1) ≤ 1 + O(n-1/3).
Joint work with Yuval Peres.
©2007 Microsoft Corporation. All rights reserved.
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