Synchronization in Interacting Reinforced Stochastic Processes

Pierre-Yves Louis (1) , Ida Germana Minelli (2)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]
2 DISIM - Department of Information Engineering, Computer Science and Mathematics = Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila]

We present a family of interacting stochastic processes introduced in [13] whose individual dynamics follow a reinforcement updating rule. This is a natural generalization of PCA dynamics on a continuous spin space. The interaction changes the long-time behavior of each process and the speed of evolution, producing a phenomenon of synchronization.

Mots clés: systems of stochastic processes; reinforcement; urn models; synchronisation

Domaines: Probabilités [math.PR]

Pierre-Yves Louis, Ida Germana Minelli. Synchronization in Interacting Reinforced Stochastic Processes. Probabilistic Cellular Automata, , 2018, 978-3-319-65556-7. ⟨10.1007/978-3-319-65558-1_8⟩. ⟨hal-01724270⟩