Walkers on the circle

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.

7 pages, 3 figures

References in corpus (7)

• The Dynamics of Crowd Disasters: An Empirical Study
• The Fundamental Diagram of Pedestrian Movement Revisited
• Basics of Modelling the Pedestrian Flow
• Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
• Scaling limit of vicious walks and two-matrix model
• Approximate Hamiltonian Statistics in One-dimensional Driven Dissipative Many-Particle Systems
• Voronoi and Voids Statistics for Super-homogeneous Point Processes

Cited by in corpus (5)

• Properties of pedestrians walking in line - Fundamental diagrams
• Properties of pedestrians walking in line: Stepping behavior
• Time-delayed Follow-the-Leader model for pedestrians walking in line
• Gaussian Determinantal Processes: a new model for directionality in data
• The Dyson and Coulomb games