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

Authors:
Béla Bollobás;Oliver Riordan
Affiliations:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 OWB, UK and Department of Mathematical Sciences, University of Memphis, Memphis Tennessee 38152;Mathematical Institute, University of Oxford, Oxford OX1, 3LB, UK
Venue:
Random Structures & Algorithms
Year:
2012

Citing 6
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Abstract

Recently, we adapted random walk arguments based on work of Nachmias and Peres, Martin-Löf, 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. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012 © 2012 Wiley Periodicals, Inc.