Walkers on the circle

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-dimensi...

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Bibliographic Details
Published in:arXiv.org 2009-12
Main Authors: Jezbera, Daniel, Kordek, David, Kriz, Jan, Seba, Petr, Sroll, Petr
Format: Article
Language:English
Subjects:
Conditioning
Pedestrians
Random walk
Random walk theory
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0909.1687