Mean-field limit for the stochastic Vicsek model

The stochastic Vicsek model arises in the study of collective motion of animals and it is receiving lots of attention due to the appearance of a phase transition

François Bolley; José A. Cañizo; José A. Carrillo

2011

Scholarcy highlights

  • The stochastic Vicsek model arises in the study of collective motion of animals and it is receiving lots of attention due to the appearance of a phase transition
  • A continuum version and variants of this model have been proposed in the recent works
  • Solutions to general SDE’s can be built in submanifolds of Rd by means of the Brownian motion of the ambient space as in for instance; one can interpret the generator in terms of the corresponding Laplace-Beltrami operator
  • Since |Vti| = |V it| = 1 for all i and t, the processest≥0 andt≥0 are solutions of the corresponding equations with bounded and Lipschitz diffusion and drifts coefficients as in

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