Functional Central Limit Theorem for the principal eigenvalue of dynamic Erd\H{o}s-R\'enyi random graphs

Rajat Subhra Hazra; Nikolai Kriukov; Michel Mandjes

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arXiv · 2407.02686

Functional Central Limit Theorem for the principal eigenvalue of dynamic Erd\H{o}s-R\'enyi random graphs

Rajat Subhra Hazra·Nikolai Kriukov·Michel Mandjes

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Abstract

In this paper we consider a dynamic version of the Erd\H{o}s-R\'{e}nyi 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.

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Rajat Subhra Hazra, Nikolai Kriukov, Michel Mandjes. 2024-07-02. Functional Central Limit Theorem for the principal eigenvalue of dynamic Erd\H{o}s-R\'enyi random graphs. https://arxiv.org/abs/2407.02686

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