Work

The process of fluctuations of the giant component of an Erdős-Rényi graph

Year: 2025

Type: article

Abstract: We consider the usual increasing process (ER(n,t∕n))0≤t≤n of Erdős-Rényi random graphs, with n vertices and mean degree t. It is well-known that when t>1, the graph ER(n,t∕n) admits a giant component whose number of vertices satisfies a central limit theorem for a fixed t when n goes to infinity. The purpose of this work is to provide a functional central limit theorem for the number of vertices of the giant component as t varies and to identify the covariance of the limiting Gaussian process.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1388

Authors: Nathanaël Enriquez, Gabriel Faraud, Sophie Lemaire

Institutions: Centre National de la Recherche Scientifique, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay, Université Paris Nanterre, Modélisation aléatoire de Paris Nanterre

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

OpenAlex ID: W4413042191

FWCI: 1.695

Cites: 16

Cited by: 1

Related to: 10