Abstract
Let C1 denote the largest connected component of the critical ErdosRényi 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).
Original language | English |
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Pages (from-to) | 1267-1286 |
Number of pages | 20 |
Journal | Annals of Probability |
Volume | 36 |
Issue number | 4 |
DOIs | |
State | Published - Jul 2008 |
Externally published | Yes |
Keywords
- Mixing time
- Percolation
- Random graphs
- Random walk