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We consider a system $x(t)=(x_{1}(t),...,x_{N}(t))$ consisting of $N$Brownian particles with synchronizing interaction between them occurring atrandom time moments $\{\tau_{n}\}_{n=1}^{\infty}$. Under assumption that thefree Brownian motions and the sequence $\{\tau_{n}\}_{n=1}^{\infty}$ areindependent we study asymptotic properties of the system when both thedimension~$N$ and the time~$t$ go to infinity. We find three time scales$t=t(N)$ of qualitatively different behavior of the system.

Time scales in large systems of Brownian particles with stochastic synchronization