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

Giacomo Aletti, Irene Crimaldi and Andrea Ghiglietti

Stochastic Processes and their Applications, 2024, vol. 176, issue C

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.

Keywords: Interacting random systems; Network-based dynamics; Reinforced stochastic processes; Urn models; Synchronization; Spectral theory; Opinion dynamics (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104427

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