Functional Central Limit Theorem for the simultaneous subgraph count of dynamic Erdős-Rényi random graphs

arXiv (Cornell University)

Abstract

In this paper we consider a dynamic Erdős-Rényi random graph with independent identically distributed edge processes. Our aim is to describe the joint evolution of the entries of a subgraph count vector. The main result of this paper is a functional central limit theorem: we establish, under an appropriate centering and scaling, the joint functional convergence of the vector of subgraph counts to a specific multidimensional Gaussian process. The result holds under mild assumptions on the edge processes, most notably a Lipschitz-type condition.

Authors 3

1. Rajat Subhra Hazra
2. Nikolai Kriukov

   University of Amsterdam

   Affiliation as printed

   Korteweg-de Vries Institute for Mathematics , University of Amsterdam , Science Park 904 , 1098 XH Amsterdam , The Netherlands

3. Michel Mandjes Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute , Leiden University , P.O. Box 9512 , 2300 RA Leiden ,