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arXiv · 2210.11347

Dyson Brownian Motion and motion by mean curvature

Ching-Peng Huang·Dominik Inauen·Govind Menon
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Abstract

We construct Dyson Brownian motion for $\beta \in (0,\infty]$ by adapting the extrinsic construction of Brownian motion on Riemannian manifolds to the geometry of group orbits within the space of Hermitian matrices. When $\beta$ is infinite, the eigenvalues evolve by Coulombic repulsion and the group orbits evolve by motion by (minus one half times) mean curvature.

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Ching-Peng Huang, Dominik Inauen, Govind Menon. 2022-10-20. Dyson Brownian Motion and motion by mean curvature. https://arxiv.org/abs/2210.11347

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