Mean-field limit for the stochastic Vicsek model

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

Research output: Contribution to journalArticleResearchpeer-review

69 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. © 2011 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)339-343
JournalApplied Mathematics Letters
Issue number3
Publication statusPublished - 1 Jan 2012


  • Collective behaviour
  • Interacting particle systems
  • Mean-field limit
  • Vicsek model


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