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arXiv · 2311.07701

The process of fluctuations of the giant component of an Erd\H{o}s-R\'enyi graph

Nathanaël Enriquez·Gabriel Faraud·Sophie Lemaire
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Abstract

We present a detailed study of the evolution of the giant component of the Erd\H{o}s-R\'enyi graph process as the mean degree increases from 1 to infinity. It leads to the identification of the limiting process of the rescaled fluctuations of its order around its deterministic asymptotic. This process is Gaussian with an explicit covariance.

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Nathanaël Enriquez, Gabriel Faraud, Sophie Lemaire. 2023-11-13. The process of fluctuations of the giant component of an Erd\H{o}s-R\'enyi graph. https://arxiv.org/abs/2311.07701

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