We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions for the emergence of some form of almost sure asymptotic synchronization. Specifically, we identify three regimes: the first involves complete synchronization, where all processes converge towards the same random variable; the second exhibits almost sure convergence of the system, but no form of synchronization subsists; and the third reveals a scenario where there is almost sure asymptotic synchronization within the cyclic classes of the interaction matrix, together with an asymptotic periodic behavior among these classes.

Networks of reinforced stochastic processes: A complete description of the first-order asymptotics

Irene Crimaldi;
2024-01-01

Abstract

We consider a finite collection of reinforced stochastic processes with a general network-based interaction among them. We provide sufficient and necessary conditions for the emergence of some form of almost sure asymptotic synchronization. Specifically, we identify three regimes: the first involves complete synchronization, where all processes converge towards the same random variable; the second exhibits almost sure convergence of the system, but no form of synchronization subsists; and the third reveals a scenario where there is almost sure asymptotic synchronization within the cyclic classes of the interaction matrix, together with an asymptotic periodic behavior among these classes.
2024
Interacting random systems, Network-based dynamics, Reinforced stochastic processes, Urn models, Synchronization, Spectral theory, Opinion dynamics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/28878
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