Nathanaël Enriquez, Gabriel Faraud, Sophie Lemaire
Published 2023-11-13Version 1
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.
On the jump of the cover time in random geometric graphs
The mixing time of the giant component of a random graph
Asymptotic normality of the size of the giant component via a random walk
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