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math.PR2009★ 2 cited
Total progeny in killed branching random walk
Louigi Addario-Berry, Nicolas Broutin
We consider a branching random walk for which the maximum position of a particle in the n'th generation, M_n, has zero speed on the linear scale: M_n/n --> 0 as n --> infinity. We…
math.PR2009★ 4 cited
The continuum limit of critical random graphs
Louigi Addario-Berry, Nicolas Broutin, Christina Goldschmidt
We consider the Erdos-Renyi random graph G(n,p) inside the critical window, that is when p=1/n+ lambda*n^{-4/3}, for some fixed lambda in R. Then, as a metric space with the graph…