Functional Central limit theorems for microscopic and macroscopic functionals of inhomogeneous random graphs

Shankar Bhamidi, Amarjit Budhiraja, Akshay Sakanaveeti

Published 2024-12-18Version 1

We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper achieves two objectives: (a) We establish functional central limit theorems for the infinite vector of microscopic type-densities and characterize the limits as infinite-dimensional Gaussian processes in a certain Banach space. (b) We establish (joint) functional central limit theorems for macroscopic observables of the giant component in the supercritical regime including size, surplus and number of vertices of various types in the giant component. Ongoing work seeks to extend these results to a broader class of inhomogeneous random graph models with general type spaces.