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Propagation of Chaos and Poisson Hypothesis

  • Communication Network Theory
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Abstract

We establish the strong Poisson hypothesis for symmetric closed networks. In particular, we prove asymptotic independence of nodes as the size of the system tends to infinity.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    A. A. Vladimirov, S. A. Pirogov, A. N. Rybko & S. B. Shlosman

  2. Skolkovo Institute of Science and Technology, Moscow, Russia

    S. B. Shlosman

  3. Aix Marseille Université, Université de Toulon, CNRS, CPT, Marseille, France

    S. B. Shlosman

Authors
  1. A. A. Vladimirov
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  2. S. A. Pirogov
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  3. A. N. Rybko
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  4. S. B. Shlosman
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Corresponding author

Correspondence to A. A. Vladimirov.

Additional information

Original Russian Text © A.A. Vladimirov, S.A. Pirogov, A.N. Rybko, S.B. Shlosman, 2018, published in Problemy Peredachi Informatsii, 2018, Vol. 54, No. 3, pp. 102–111.

The research of A. Rybko and A. Vladimirov (the results of Sections 3–5) was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.

The research of S. Pirogov, presented in Section 6, was carried out at the expense of the Russian Science Foundation, project no. 17-11-01098.

The work of S. Shlosman, presented in Sections 1–2, was performed in the framework of the Labex Archimede (ANR-11-LABX-0033) and the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Avenir” French Government programme managed by the French National Research Agency (ANR); it was also supported by the Grant PRC no. 1556 CNRS-RFBR 2017–2019 “Multidimensional semi-classical problems of condensed matter physics and quantum mechanics.”

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Vladimirov, A.A., Pirogov, S.A., Rybko, A.N. et al. Propagation of Chaos and Poisson Hypothesis. Probl Inf Transm 54, 290–299 (2018). https://doi.org/10.1134/S0032946018030080

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  • DOI: https://doi.org/10.1134/S0032946018030080