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

TL;DR

This paper rigorously proves the mean field limit and propagation of chaos for a two-dimensional pedestrian flow model, demonstrating convergence of particle systems to a Vlasov equation solution using probabilistic methods.

Contribution

It provides the first rigorous proof of the mean field limit for a pedestrian flow model coupled with the eikonal equation, including stochastic initial data and convergence in probability.

Findings

Convergence of particle system to Vlasov equation in probability

Propagation of chaos established in bounded Lipschitz distance

Validates the mean field approximation for pedestrian flow models

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.