Moderate deviations for the size of the giant component in a random hypergraph

Abstract

We prove a moderate deviations principles for the size of the largest connected component in a random $d$-uniform hypergraph. The key tool is a version of the exploration process, that is also used to investigate the giant component of an Erdös-Rényi graph, a moderate deviations principle for the martingale associated with this exploration process, and exponential estimates.

28 pages