%D 2017
%K Keywords: Interacting Systems; Reinforced Stochastic Processes; Urn Models; Complex Networks; Synchronization; Asymptotic Normality. - 
2010 AMS classification: 60F05, 60F15, 60K35, 62P35, 91D30
%I The Institute of Mathematical Statistics
%T Synchronization of Reinforced Stochastic Processes with a Network-based Interaction
%N 6
%V 27
%R doi:10.1214/17-AAP1296
%L eprints3699
%X Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the tendency of different components to adopt a common behavior. We continue the study of a model of interacting stochastic processes with reinforcement, that
recently has been introduced in [21]. Generally speaking, by reinforcement we mean any mechanism for which the probability that a given event occurs has an increasing dependence on the number of times that events of the same type occurred in the past. The particularity of systems of such interacting stochastic processes is that synchronization is induced along time by the reinforcement mechanism itself and does not require a large-scale limit. We focus on the relationship between the topology of the network of the interactions and the long-time synchronization phenomenon. After proving the almost sure synchronization, we provide some CLTs in the sense
of stable convergence that establish the convergence rates and the asymptotic distributions for both convergence to the common limit and synchronization. The obtained results lead to the construction of asymptotic confidence intervals for the limit random variable and of statistical tests to make inference on the topology of the network.
%J The Annals of Applied Probability
%P 3787-3844
%A Giacomo Aletti
%A Irene Crimaldi
%A Andrea Ghiglietti