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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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/

[1] Manita A., Shcherbakov V., “Asymptotic analysis of a particle system with mean-field interaction”, Markov Process. Related Fields, 11:3 (2005), 489–518 | MR | Zbl

[2] Malyshev V. A., Manita A. D., “Fazovye perekhody v modeli sinkhronizatsii vremeni”, Teoriya veroyatn. i ee primen., 50:1 (2005), 150–158 | MR

[3] Malyshev V., Manita A., “Asymptotic behavior of the time synchronization model”, Representation Theory, Dynamical Systems, and Asymptotic Combinatorics, Amer. Math. Soc. Transl. Ser. 2, 217, Amer. Math. Soc., Providence, 2006, 101–115 | MR | Zbl

[4] Malyshkin A. G., “Predelnaya dinamika dlya veroyatnostnykh modelei obmena informatsiei v setyakh parallelnykh vychislenii”, Problemy peredachi informatsii, 42:3 (2006), 78–96 | MR

[5] Manita A., Simonot F., “Clustering in stochastic asynchronous algorithms for distributed simulations”, Lecture Notes in Comput. Sci., 3777, 2005, 26–37 | Zbl

[6] Mitra D., Mitrani I., “Analysis and optimum performance of two message-passing parallel processors synchronized by rollback”, Performance Evaluation, 7:2 (1987), 111–124 | DOI | MR | Zbl