Walkers on the circle

TL;DR

This paper shows that when pedestrians are unable to avoid each other, the statistical distribution of their distances aligns with the Gaussian Unitary Ensemble, similar to non-intersecting random walks, revealing a universal behavior.

Contribution

It experimentally demonstrates that hindered pedestrians exhibit statistical properties matching non-intersecting random walks, linking human movement to random matrix theory.

Findings

Distances follow GUE statistics when avoidance is hindered

Behavior resembles non-intersecting random walks

Universal statistical properties observed in pedestrian dynamics

Abstract

We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been obtained for an $n$-tuple of non-intersecting (one-dimensional, unidirectional) random walks. Thus, the observed behavior of autonomous walkers conditioned not to cross their trajectories (or, in other words, to stay in strict order at any time) resembles non-intersecting random walks.