As I've mentioned a few times, you can use eigenvalues of random matrices to model random walks of points with repulsive forces. Here's a really nice application: modelling the bus system in Cuernavaca, Mexico https://authors.library.caltech.edu/3946/1/BAIjpa06.pdf …https://twitter.com/sigfpe/status/986298301975678976 …
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The probability density is of the form exp(-H) where H is the Hamiltonian. The repulsion term is part of H
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