4 citations · 6 across the 2 of their papers we have counts for
2 papers
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…