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## Stochastic Synchronization in a Large System of Identical Particles

Theory of Probability and Its Applications. 2009. Vol. 53. No. 1. P. 155-161.

We consider a basic stochastic particle system consisting of N identical particles with isotropic k-particle synchronization, ${k\ge 2}$. In the limit when both the number of particles N and the time $t=t(N)$ grow to infinity we study an asymptotic behavior of a coordinate spread of the particle system. We describe three time stages of $t(N)$ for which a qualitative behavior of the system is completely different. Moreover, we discuss the case when a spread of the initial configuration depends on N and increases to infinity as $N\rightarrow\infty$.