Geodesic
Random walk of a “drunk company"
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 2, pp. 350-359 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Brownian agent, stochastic dynamics, functional integration method. 
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     author = {A. G. Semenov},
     title = {Random walk of a~{\textquotedblleft}drunk company"},
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A. G. Semenov. Random walk of a “drunk company". Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 2, pp. 350-359. http://geodesic.mathdoc.fr/item/TMF_2016_187_2_a9/

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