On the largest component of the critical random digraph

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Matthew Coulson

Abstract

We consider the largest component 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 probabilities that $|\mathcal{C}_1|n^{-1/3}$ is very large or very small that are analogous to those given by Nachmias and Peres for $G(n,p)$.

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How to Cite
Coulson, M. (2019). On the largest component of the critical random digraph. Acta Mathematica Universitatis Comenianae, 88(3), 567-572. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1184/695
Section
EUROCOMB 2019