most citedCritical percolation on random regular graphs

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math.PR2007★ 2 cited

Mean-field conditions for percolation on finite graphs

Asaf Nachmias

Let G_n be a sequence of finite transitive graphs with vertex degree d=d(n) and |G_n|=n. Denote by p^t(v,v) the return probability after t steps of the non-backtracking random walk…

math.PR2007★ 4 cited

Critical percolation on random regular graphs

Asaf Nachmias, Yuval Peres

We describe the component sizes in critical independent p-bond percolation on a random d-regular graph on n vertices, where d \geq 3 is fixed and n grows. We prove mean-field behav…