  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 $\{\tau_{n}\}_{n=1}^{\infty}$. Under assumption that the
free Brownian motions and the sequence $\{\tau_{n}\}_{n=1}^{\infty}$ 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.
