Mean-field limit for the stochastic Vicsek model

Details Mean-field limit for the stochastic Vicsek model Mean-field limit for the stochastic Vicsek model

2011-02-07

arxiv.org/abs/1102.1325v1

Applied Mathematics Letters, Vol. 25, No. 3, pp. 339-343 (2011)

Mathematics

Probability

Scientific paper

10.1016/j.aml.2011.09.011

We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behavior of individuals with a fixed speed. We rigorously derive the kinetic mean-field partial differential equation satisfied when the number N of particles tends to infinity, quantifying the convergence of the law of one particle to the solution of the PDE. For this we adapt a classical coupling argument to the present case in which both the particle system and the PDE are defined on a surface rather than on the whole space. As part of the study we give existence and uniqueness results for both the particle system and the PDE.

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