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.File | Dimensione | Formato | |
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arXiv-2206.07514-v4.pdf
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SPA1-1-s2.0-S0304414924001339-main.pdf
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