Time scales in large systems of Brownian particles with stochastic synchronization

Details Time scales in large systems of Brownian particles with stochastic synchronization Time scales in large systems of Brownian particles with stochastic synchronization

2010-12-14

arxiv.org/abs/1012.3140v1

Mathematics

Probability

12 pages

Scientific paper

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.

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