Interacting stochastic processes with local/global reinforcement schemes

International audienceThe Polya urn is a well known reinforcement stochastic process leading to a random (beta-distributed) time-asymptotics. The Friedman urn is a modification whose time-limit is not random anymore. We consider a (finite-) system of interacting reinforced stochastic processes mixing these two schemes with different strength. Individual components are updated through a competition between a local reinforcement rule and a global one, defined as transformation of the average state (mean field). We study the time-asymptotics and synchronisation phenomenon according to the different parameter regimes