Asymptotic normality of the size of the giant component via a random walk

Bela Bollobas; Oliver Riordan

doi:10.1016/j.jctb.2011.04.003

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arXiv · 1010.4595

Asymptotic normality of the size of the giant component via a random walk

Bela Bollobas·Oliver Riordan

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Abstract

In this paper we give a simple new proof of a result of Pittel and Wormald concerning the asymptotic value and (suitably rescaled) limiting distribution of the number of vertices in the giant component of $G(n,p)$ above the scaling window of the phase transition. Nachmias and Peres used martingale arguments to study Karp's exploration process, obtaining a simple proof of a weak form of this result. We use slightly different martingale arguments to obtain a much sharper result with little extra work.

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Bela Bollobas, Oliver Riordan. 2010-10-21. Asymptotic normality of the size of the giant component via a random walk. https://doi.org/10.1016/j.jctb.2011.04.003

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