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

Journal article

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.

Authors: Bollobás, B; Riordan, O

• Journal: Random Structures and Algorithms
• Volume: 41
• Issue: 4
• Pages: 441-450
• Publication date: 2012-12-01
• DOI: 10.1002/rsa.20456
• EISSN: 1098-2418
• ISSN: 1042-9832
• Language: English
• Keywords: Martingale; Random hypergraph; Phase transition