Synchronization via interacting reinforcement

Abstract

We consider a system of urns of Polya-type, with balls of two colors; the reinforcement of each urn depends both on the content of the same urn and on the average content of all urns. We show that the urns synchronize almost surely, in the sense that the fraction of balls of a given color converges almost surely, as the time goes to infinity, to the same limit for all urns. A normal approximation for a large number of urns is also obtained.

References in corpus (4)

• A survey of random processes with reinforcement
• Metastability in Interacting Nonlinear Stochastic Differential Equations I: From Weak Coupling to Synchronisation
• Self Organization of Interacting Polya Urns
• Generalized Interacting Urn Models

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• Networks of reinforced stochastic processes: asymptotics for the empirical means
• Generalized Rescaled Polya urn and its statistical applications
• Networks of reinforced stochastic processes: a complete description of the first-order asymptotics
• Urns with Multiple Drawings and Graph-Based Interaction
• Stable Configurations in Social Networks