Path-integral representation of diluted pedestrian dynamics
Abstract
We frame the issue of pedestrian dynamics modeling in terms of path-integrals, a formalism originally introduced in quantum mechanics to account for the behavior of quantum particles, later extended to quantum field theories and to statistical physics. Path-integration enables a trajectory-centric representation of the pedestrian motion, directly providing the probability of observing a given trajectory. This appears as the most natural language to describe the statistical properties of pedestrian dynamics in generic settings. In a given venue, individual trajectories can belong to many possible usage patterns and, within each of them, they can display wide variability. We provide first a primer on path-integration, and we introduce and discuss the path-integral functional probability measure for pedestrian dynamics in the diluted limit. As an illustrative example, we connect the path-integral description to a Langevin model that we developed previously for a particular crowd flow condition (the flow in a narrow corridor). Building on our previous real-life measurements, we provide a quantitatively correct path-integral representation for this condition. Finally, we show how the path-integral formalism can be used to evaluate the probability of rare-events (in the case of the corridor, U-turns).
Cite
@article{arxiv.1804.03634,
title = {Path-integral representation of diluted pedestrian dynamics},
author = {Alessandro Corbetta and Federico Toschi},
journal= {arXiv preprint arXiv:1804.03634},
year = {2020}
}