Journal of Statistical Physics

, Volume 166, Issue 2, pp 211–229 | Cite as

Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model

Article

Abstract

In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation on the microscopic scale. For stochastic initial data, it is proved that the solution of the N-particle pedestrian flow system with properly chosen cut-off converges in the probability sense to the solution of the characteristics of the non-cut-off Vlasov equation. Furthermore, the result on propagation of chaos is also deduced in terms of bounded Lipschitz distance.

Keywords

Probabilistic method Pedestrian flow Mean field limit Vlasov equation Propagation of chaos 

Mathematics Subject Classification

35Q83 82C22 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MannheimMannheimGermany

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