The phase transition in a random hypergraph

摘要

We show that in the evolution of the random d-uniform hypergraph Gd(n,M) the phase transition occurs when M=n/d(d−1)+O(n2/3). We also prove local limit theorems for the distribution of the size of the largest component of Gd(n,M) in the subcritical and in the early supercritical phase.