Functional central limit theorem for the simultaneous subgraph count of dynamic Erdős–Rényi random graphs

Electronic Journal of Probability, vol. 30, pp. 1–38

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 Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

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

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