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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 1, Pages 150–158 (Mi tvp163)  

This article is cited in 6 scientific papers (total in 6 papers)

Short Communications

Phase transitions in the time synchronization model

V. A. Malyshev, A. D. Manita

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

DOI: https://doi.org/10.4213/tvp163

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English version:
Theory of Probability and its Applications, 2006, 50:1, 1334–141

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Received: 09.09.2004

Citation: V. A. Malyshev, A. D. Manita, “Phase transitions in the time synchronization model”, Teor. Veroyatnost. i Primenen., 50:1 (2005), 150–158; Theory Probab. Appl., 50:1 (2006), 1334–141

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. Malyshkin, “Limit Dynamics for Stochastic Models of Data Exchange in Parallel Computation Networks”, Problems Inform. Transmission, 42:3 (2006), 234–250  mathnet  crossref  mathscinet  elib  elib
    2. A. D. Manita, “Stochastic Synchronization in a Large System of Identical Particles”, Theory Probab. Appl., 53:1 (2009), 155–161  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Manita A., “Brownian Particles Interacting via Synchronizations”, Comm Statist Theory Methods, 40:19–20 (2011), 3440–3451  crossref  mathscinet  zmath  isi  elib  scopus
    4. Manita A., “Clock Synchronization in Symmetric Stochastic Networks”, Queueing Syst., 76:2, SI (2014), 149–180  crossref  mathscinet  zmath  isi  scopus
    5. V. V. Karpushin, “Convergence rate in stochastic particle systems with synchronization”, Theory Probab. Appl., 61:2 (2017), 345–355  mathnet  crossref  crossref  mathscinet  isi  elib
    6. Manita A., “On Behavior of Stochastic Synchronization Models”, International Conference on Computer Simulation in Physics and Beyond 2015, Journal of Physics Conference Series, 681, IOP Publishing Ltd, 2016, 012024  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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