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The critical window in random digraphs
Published online by Cambridge University Press: 08 October 2021
Abstract
We consider the component structure of the random digraph D(n,p) inside the critical window
$p = n^{-1} + \lambda n^{-4/3}$
. We show that the largest component
$\mathcal{C}_1$
has size of order
$n^{1/3}$
in this range. In particular we give explicit bounds on the tail probabilities of
$|\mathcal{C}_1|n^{-1/3}$
.
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- © The Author(s), 2021. Published by Cambridge University Press
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