Susceptibility in subcritical random graphs

We study the evolution of the susceptibility in the subcritical random graph G(n,p) as n tends to infinity. We obtain precise asymptotics of its expectation and variance and show that it obeys a law of large numbers. We also prove that the scaled fluctuations of the susceptibility around its deterministic limit converge to a Gaussian law. We further extend our results to higher moments of the component size of a random vertex and prove that they are jointly asymptotically normal.

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