Geodesic
Stochastic Synchronization in a Large System of Identical Particles
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 162-168

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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 $N\to\infty$.
Keywords: interacting particle systems, multidimensional Markov processes, stochastic synchronization, mean-field models.
Mots-clés : $k$-particle interactions 
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     author = {A. D. Manita},
     title = {Stochastic {Synchronization} in a {Large} {System} of {Identical} {Particles}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {162--168},
     publisher = {mathdoc},
     volume = {53},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a9/}
}
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A. D. Manita. Stochastic Synchronization in a Large System of Identical Particles. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 162-168. http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a9/