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

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 Erd"os-R'enyi graph, a moderate deviations principle for the martingale associated with this exploration process, and exponential estimates.