2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124470We consider a basic stochastic particle system consisting of $N$ identical particles with isotropic $k$-particle synchronization, $k\geq 2$. In the limit when both number of particles $N$ and 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\to \infty $.9 pages, 1 figure; one reference and one figure added, typos corrected, minor improvements of the proofsProbability60K35; 60J27text