Fluctuations of the giant of Poisson random graphs

Abstract

Enriquez, Faraud, and Lemaire (2023) have established process-level fluctuations for the giant of the dynamic Erdős-Rényi random graph above criticality and show that the limit is a centered Gaussian process with continuous sample paths. A random walk proof was recently obtained by Corujo, Limic and Lemaire (2024). We show that a similar result holds for rank-one inhomogeneous models whenever the empirical weight distribution converges to a limit and its second moment converges as well.

13 pages