Geodesic
Phase transitions in the time synchronization model
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 1, pp. 150-158

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There are two types $i=1,2$ of particles on the line $R$, with $N_i$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_i$. Moreover, any particle of type $i=1,2$ jumps to any particle of type $j=1,2$ with rates $N_{j}^{-1}\alpha _{ij}$. We find phase transitions in the clusterization (synchronization) behavior of this system of particles on different time scales $t=t(N)$ relative to $N=N_1+N_2$.
Keywords: Markov process, stochastic particles system, synchronization model. 
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     author = {V. A. Malyshev and A. D. Manita},
     title = {Phase transitions in the time synchronization model},
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     publisher = {mathdoc},
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     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_1_a8/}
}
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V. A. Malyshev; A. D. Manita. Phase transitions in the time synchronization model. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 1, pp. 150-158. http://geodesic.mathdoc.fr/item/TVP_2005_50_1_a8/