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

TL;DR

This paper extends a probabilistic method to prove that the size of the giant component in random hypergraphs follows a normal distribution in the supercritical regime, broadening understanding beyond previous partial results.

Contribution

It demonstrates that the method used for random graphs also applies to hypergraphs, establishing asymptotic normality throughout the supercritical phase.

Findings

Proves asymptotic normality of the giant component in hypergraphs.

Extends previous results from graph models to hypergraph models.

Applies a unified probabilistic approach to different random structures.

Abstract

Recently, we adapted random walk arguments based on work of Nachmias and Peres, Martin-L\"of, 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.