Abstract
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
$|\mathcal{C}_1|n^{-1/3}$
.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Cited by
2 articles.
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1. The birth of the strong components;Random Structures & Algorithms;2023-08-07
2. The scaling limit of a critical random directed graph;The Annals of Applied Probability;2023-06-01