Abstract
We consider a system x(t) = (x 1(t),…, x N (t)) consisting of N Brownian particles with synchronizing interaction between them occurring at random time moments . Under assumption that the free Brownian motions and the sequence are independent we study asymptotic properties of the system when both the dimension N and the time t go to infinity. We find three time scales t = t(N) of qualitatively different behavior of the system.
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