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Random walk of a “drunk company”

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Abstract

We study the collective behavior of a system of Brownian agents each of which moves orienting itself to the group as a whole. This system is the simplest model of the motion of a “united drunk company.” For such a system, we use the functional integration technique to calculate the probability of transition from one point to another and to determine the time dependence of the probability density to find a member of the “drunk company” near a given point. It turns out that the system exhibits an interesting collective behavior at large times and this behavior cannot be described by the simplest mean-field-type approximation. We also obtain an exact solution in the case where one of the agents is “sober” and moves along a given trajectory. The obtained results are used to discuss whether such systems can be described by different theoretical approaches.

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Authors and Affiliations

  1. Tamm Department of Theoretical Physics, Lebedev Physical Institute, RAS, Moscow, Russia

    A. G. Semenov

  2. Russian Endowment for Education and Science, Moscow, Russia

    A. G. Semenov

  3. National Research University Higher School of Economics, Moscow, Russia

    A. G. Semenov

Authors
  1. A. G. Semenov
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Correspondence to A. G. Semenov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 187, No. 2, pp. 350–359, May, 2016.

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Semenov, A.G. Random walk of a “drunk company”. Theor Math Phys 187, 753–761 (2016). https://doi.org/10.1134/S0040577916050111

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  • DOI: https://doi.org/10.1134/S0040577916050111

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