Time scales in large systems of Brownian particles with stochastic synchronization

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 $\{{\tau }_n{\}}_{n=1}^{\infty }$. 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.

12 pages

Cited by in corpus (1)

• Time Scales in Probabilistic Models of Wireless Sensor Networks