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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.
Publication status:
Published

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Publisher copy:
10.1016/j.jctb.2011.04.003

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Journal:
J. Combinatorial Theory B 102 (2012), 53--61
Volume:
102
Issue:
1
Pages:
53-61
Publication date:
2010-10-21
DOI:
EISSN:
1096-0902
ISSN:
0095-8956
URN:
uuid:0fbf81c4-e38c-4bbc-8a87-b74f4db3fb74
Source identifiers:
216373
Local pid:
pubs:216373
Language:
English
Keywords:

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