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

Bela Bollobas; Oliver Riordan

doi:10.1002/rsa.20456

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arXiv · 1112.3615

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

Bela Bollobas·Oliver Riordan

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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.

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Bela Bollobas, Oliver Riordan. 2011-12-15. Asymptotic normality of the size of the giant component in a random hypergraph. https://doi.org/10.1002/rsa.20456

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