The Order of the Giant Component of Random Hypergraphs

Abstract

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.

28 pages, 1 figure

References in corpus (1)

• Local Limit Theorems and Number of Connected Hypergraphs

Cited by in corpus (9)

• Local limit theorems via Landau-Kolmogorov inequalities
• Asymptotic normality of the size of the giant component in a random hypergraph
• Evolution of high-order connected components in random hypergraphs
• Exploring hypergraphs with martingales
• Counting connected hypergraphs via the probabilistic method
• Local limit theorems for subgraph counts
• Connectivity of random hypergraphs with a given hyperedge size distribution
• Counting dense connected hypergraphs via the probabilistic method
• Asymptotic distribution of the numbers of vertices and arcs of the giant strong component in sparse random digraphs