%0 Journal Article
%T Asymptotic normality of the size of the giant component via a random walk
%A Bela Bollobas
%A Oliver Riordan
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.jctb.2011.04.003
%X 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.
%U http://arxiv.org/abs/1010.4595v2