In this paper we consider two-opinion voter models on dynamic random graphs,in which the joint dynamics of opinions and graphs acts as one-way feedback,i.e., edges appear and disappear over time depending on the opinions of the twoconnected vertices, while the opinion dynamics does not depend on the edgeprocess. Our goal is to investigate the joint evolution of the entries of avoter subgraph count vector, i.e., vector of subgraphs where each vertex has aspecific opinion, in the regime that the number of vertices grows large. Themain result of this paper is a functional central limit theorem. In particular,we prove that, under a proper centering and scaling, the joint functional ofthe vector of subgraph counts converges to a specific multidimensional Gaussianprocess.
Functional central limit theorem for the subgraph count of the voter model on dynamic random graphs
Simone Baldassarri
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2025-01-01
Abstract
In this paper we consider two-opinion voter models on dynamic random graphs,in which the joint dynamics of opinions and graphs acts as one-way feedback,i.e., edges appear and disappear over time depending on the opinions of the twoconnected vertices, while the opinion dynamics does not depend on the edgeprocess. Our goal is to investigate the joint evolution of the entries of avoter subgraph count vector, i.e., vector of subgraphs where each vertex has aspecific opinion, in the regime that the number of vertices grows large. Themain result of this paper is a functional central limit theorem. In particular,we prove that, under a proper centering and scaling, the joint functional ofthe vector of subgraph counts converges to a specific multidimensional Gaussianprocess.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
