Аннотация: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)(infinity). Under assumption that the free Brownian motions and the sequence tau(n)(n=1)(infinity) 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.