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.
Recently, Bollobás and Riordan established the (properly rescaled and centered) number of vertices in the giant component in H d (n, p) converges in distribution to the normal distribution throughout the supercritical regime, using the same arguments as in REF .
Asymptotic normality of the size of the giant component in a random hypergraph
Random Struct. Algorithms 41 (2012), 441--450
Mathematics Computer Science