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

2019/07/18 by Jingjia Liu, Matthias Löwe, Liu, Jingjia +1
Mathematics · #60F10 (Primary) 05C65 (Secondary) #FOS: Mathematics #Limits and Structures in Graph Theory #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1907.07834

openalex publication_date 2019/07/18 · openalex created_date 2019/07/23 · openalex updated_date 2026/07/28

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.

Related

• The size of the giant component in random hypergraphs
• A large deviation principle for the Erdős-Rényi uniform random graph
• Regularity method and large deviation principles for the Erdős--Rényi hypergraph
• Component sizes of the random graph outside the scaling window
• An alternative approach to large deviations for the almost-critical Erdős-Rényi random graph