Dyson Brownian Motion and motion by mean curvature

2022/10/20 by Huang, Ching-Peng, Inauen, Dominik, Menon, Govind · 2 citations
#15B51 #53E10 #60D05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2210.11347

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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