The Order of the Giant Component of Random Hypergraphs

Michael Behrisch, Amin Coja-Oghlan, Mihyun Kang

Published 2007-06-04Version 1

We establish central and local limit theorems for the number of vertices in the largest component of a random $d$-uniform hypergraph $\hnp$ with edge probability $p=c/\binnd$, where $(d-1)^{-1}+\eps<c<\infty$. The proof relies on a new, purely probabilistic approach, and is based on Stein's method as well as exposing the edges of $H_d(n,p)$ in several rounds.