Asymptotic normality of the size of the giant component via a random walk
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. © 2011 Elsevier Inc.
Publication Title
Journal of Combinatorial Theory. Series B
Recommended Citation
Bollobás, B., & Riordan, O. (2012). Asymptotic normality of the size of the giant component via a random walk. Journal of Combinatorial Theory. Series B, 102 (1), 53-61. https://doi.org/10.1016/j.jctb.2011.04.003
