Dyson Brownian Motion and motion by mean curvature
Abstract
We construct Dyson Brownian motion for β ∈ (0,∞] 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.
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