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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As an example, see the repulsion factor on page 15 here: https://arxiv.org/pdf/1712.07903.pdf …
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I sort of wondered what the Hamiltonian was
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