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Asymptotic normality of the size of the giant component in a random hypergraph

Abstract:
Recently, we adapted random walk arguments based on work of Nachmias and Peres, Martin-L\"of, Karp and Aldous to give a simple proof of the asymptotic normality of the size of the giant component in the random graph $G(n,p)$ above the phase transition. Here we show that the same method applies to the analogous model of random $k$-uniform hypergraphs, establishing asymptotic normality throughout the (sparse) supercritical regime. Previously, asymptotic normality was known only towards the two ends of this regime.
Publication status:
Published

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Publisher copy:
10.1002/rsa.20456

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Journal:
Random Struct. Algorithms 41 (2012), 441--450
Volume:
41
Issue:
4
Pages:
441-450
Publication date:
2011-12-15
DOI:
EISSN:
1098-2418
ISSN:
1042-9832
URN:
uuid:9f4ab76f-e593-4eda-84c0-9e5a1918063b
Source identifiers:
221445
Local pid:
pubs:221445
Keywords:

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