Functional central limit theorem for the principal eigenvalue of dynamic Erdős–Rényi random graphs

The Annals of Applied Probability, vol. 36, pp. 2468–2498

Abstract

In this paper we consider a dynamic version of the Erdős–Rényi random graph, in which edges independently appear and disappear in time, with the on- and off times being exponentially distributed. The focus lies on the evolution of the principle eigenvalue of the adjacency matrix in the regime that the number of vertices grows large. The main result is a functional central limit theorem, which displays that the principal eigenvalue essentially inherits the characteristics of the dynamics of the individual edges.

Authors 3

1. Rajat Subhra Hazra Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University

2. Nikolai Kriukov

   University of Amsterdam

   Affiliation as printed

   Korteweg-de Vries Institute for Mathematics, University of Amsterdam

3. Michel Mandjes Aachen Mathematical Institute

   Leiden University

   Affiliation as printed

   Mathematical Institute, Leiden University