Abstract
We construct Dyson Brownian motion for by adapting the extrinsic construction of Brownian motion on Riemannian manifolds to the geometry of group orbits within the space of Hermitian matrices. When β is infinite, the eigenvalues evolve by Coulombic repulsion and the group orbits evolve by motion by (minus one half times) mean curvature.
Funding Statement
Supported by the National Science Foundation (DMS 2107205).
Citation
Ching-Peng Huang. Dominik Inauen. Govind Menon. "Motion by mean curvature and Dyson Brownian Motion." Electron. Commun. Probab. 28 1 - 10, 2023. https://doi.org/10.1214/23-ECP540
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