The order of the giant component of random hypergraphs
By Michael Behrisch and Amin Coja-Oghlan and Mihyun KangSubmitted
Abstract
Let Hd(n,p) denote a random d-uniform hypergraph with n vertices in which each of the possible edges is present with probability p=p(n) independently, and let Hd(n,m) denote a uniformly distributed d-uniform hypergraph with n vertices and m edges. We establish central and local limit theorems for the number of vertices in the largest component of Hd(n,p). The proof relies on a new, purely probabilistic approach, and is based on Stein's method as well as exposing the edges of Hd(n,p) in several rounds.
