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The process of fluctuations of the giant component of an Erd\H{o}s-R\'enyi graph
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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.
Forward citations
Cited by 2 Pith papers
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Fluctuations of the giant of Poisson random graphs
The giant component of supercritical rank-one random graphs has process-level Gaussian fluctuations, with an explicit covariance given by the limiting weight distribution.
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A central limit theorem for the giant in a stochastic block model
Derives an explicit Gaussian central limit theorem for the giant component in a supercritical finite-type stochastic block model, via the excursion representation of the breadth-first walk.
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