Dyson Brownian Motion and motion by mean curvature
arXiv:2210.11347
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 is infinite, the eigenvalues evolve by Coulombic repulsion and the group orbits evolve by motion by (minus one half times) mean curvature.