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arXiv · 1610.04043

Barak-Erd\H{o}s graphs and the infinite-bin model

Bastien Mallein·Sanjay Ramassamy
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Abstract

A Barak-Erd\H{o}s graph is a directed acyclic version of the Erd\H{o}s-R\'enyi random graph. It is obtained by performing independent bond percolation with parameter $p$ on the complete graph with vertices $\{1,...,n\}$, in which the edge between two vertices $i 1/2$, and compute its power series expansion. We also obtain the first two terms of the asymptotic expansion of $C$ as $p \to 0$, using a coupling with branching random walks.

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Bastien Mallein, Sanjay Ramassamy. 2016-10-13. Barak-Erd\H{o}s graphs and the infinite-bin model. https://doi.org/10.1214/20-aihp1141

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