English

Dyson Brownian Motion and motion by mean curvature

Probability 2023-05-22 v4

Abstract

We construct Dyson Brownian motion for β(0,]\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 β\beta is infinite, the eigenvalues evolve by Coulombic repulsion and the group orbits evolve by motion by (minus one half times) mean curvature.

Keywords

Cite

@article{arxiv.2210.11347,
  title  = {Dyson Brownian Motion and motion by mean curvature},
  author = {Ching-Peng Huang and Dominik Inauen and Govind Menon},
  journal= {arXiv preprint arXiv:2210.11347},
  year   = {2023}
}