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

Rajat Subhra Hazra; Nikolai Kriukov; Michel Mandjes

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arXiv · 2502.01259

Functional Central Limit Theorem for the simultaneous subgraph count 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 Erd\H{o}s-R\'{e}nyi 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.

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Rajat Subhra Hazra, Nikolai Kriukov, Michel Mandjes. 2025-02-03. Functional Central Limit Theorem for the simultaneous subgraph count of dynamic Erd\H{o}s-R\'enyi random graphs. https://arxiv.org/abs/2502.01259

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