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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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arxiv 2311.07701 v2 pith:DPYRFP7D submitted 2023-11-13 math.PR math.CO

classification math.PRmath.CO
keywords processcomponentenyifluctuationsgiantgrapharoundasymptotic
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fluctuations of the giant of Poisson random graphs

    math.PR 2025-01 conditional novelty 6.0 of 10

    The giant component of supercritical rank-one random graphs has process-level Gaussian fluctuations, with an explicit covariance given by the limiting weight distribution.

  2. A central limit theorem for the giant in a stochastic block model

    math.PR 2025-01 conditional novelty 6.0 of 10

    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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