Mean-field limit for the stochastic Vicsek model

François Bolley, José A. Cañizo, José A. Carrillo

Research output: Contribution to journalArticlepeer-review

63 Citations (Scopus)


We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behaviour 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 Rd. As part of the study we give existence and uniqueness results for both the particle system and the PDE.
Original languageEnglish
Pages (from-to)339-343
Number of pages5
JournalApplied Mathematics Letters
Issue number3
Publication statusPublished - 1 Mar 2012


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