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

## TL;DR

This paper establishes moderate deviations principles for the size of the largest connected component in a random hypergraph, extending techniques from Erdős-Rényi graphs to hypergraphs using exploration processes and martingale analysis.

## Contribution

It introduces a novel moderate deviations framework for hypergraph giant components, adapting exploration process methods and martingale techniques from graph theory.

## Key findings

- Proves moderate deviations principles for hypergraph giant components
- Develops exponential estimates for exploration process martingales
- Extends Erdős-Rényi graph methods to hypergraphs

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