Mean-field limit for the stochastic Vicsek model
Probability
2011-12-06 v1 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.1102.1325,
title = {Mean-field limit for the stochastic Vicsek model},
author = {François Bolley and José A. Cañizo and José A. Carrillo},
journal= {arXiv preprint arXiv:1102.1325},
year = {2011}
}