Replica-mean-field limits of fragmentation-interaction-aggregation processes
نویسندگان
چکیده
Network dynamics with point-process-based interactions are of paramount modeling interest. Unfortunately, most relevant involve complex graphs for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas networks In limit infinite number replicas, these become analytically tractable under so-called "Poisson Hypothesis". However, in applications, hypothesis only conjectured. Here, we establish Poisson Hypothesis a general class discrete-time, dynamics, that propose to call fragmentation-interaction-aggregation processes, and introduced present paper. These processes feature network nodes, each endowed state governing their random activation. Each activation triggers fragmentation activated node transmission interaction signals downstream nodes. turn, received by nodes aggregated state. Our main contribution proof version any class. The obtained establishing propagation asymptotic independence variables replicas. Discrete time Galves-L\"{o}cherbach neural used as basic instance illustration our analysis.
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ژورنال
عنوان ژورنال: Journal of Applied Probability
سال: 2022
ISSN: ['1475-6072', '0021-9002']
DOI: https://doi.org/10.1017/jpr.2021.31