Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model
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.
KeywordsProbabilistic method Pedestrian flow Mean field limit Vlasov equation Propagation of chaos
Mathematics Subject Classification35Q83 82C22
This work was financially supported by the DAAD project “DAAD-PPP VR China” (Project-ID: 57215936).
- 11.Jabin, P.E., Hauray, M.: Particles approximations of Vlasov equations with singular forces: propagation of chaos. arXiv preprint (2014). arXiv:1107.3821
- 12.Lewin, K.: In: D. Cartwright (eds.) Field Theory in Social Science: Selected Theoretical Papers. Harper and Brothers, New York (1951)Google Scholar
- 17.Sznitman, A.S.: Topics in propagation of chaos. In: Ecole d’été de probabilités de Saint-Flour XIX-1989. Springer, Berlin, pp. 165–251 (1991)Google Scholar