most citedCritical random graphs: Diameter and mixing time

113 citations · 117 across the 2 of their papers we have counts for

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math.PR2009★ 4 cited

Is the critical percolation probability local?

Itai Benjamini, Asaf Nachmias, Yuval Peres

We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular…

math.PR2007★ 113 cited

Critical random graphs: Diameter and mixing time

Asaf Nachmias, Yuval Peres

Let denote the largest connected component of the critical Erdős--Rényi random graph . We show that, typically, the diameter of …

math.PR2006★ 34 cited

Component sizes of the random graph outside the scaling window

Asaf Nachmias, Yuval Peres

We provide simple proofs describing the behavior of the largest component of the Erdos-Renyi random graph G(n,p) outside of the scaling window, p={1+\eps(n) \over n} where \eps(n)…