Functional Central Limit Theorem for the principal eigenvalue of dynamic Erdős-Rényi random graphs

arXiv (Cornell University)

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 , P.O. Box 9512 , 2300 RA Leiden , The Netherlands ,

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 · University of Amsterdam

   Affiliation as printed

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

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