Motion by mean curvature and Dyson Brownian Motion

Ching-Peng Huang; Dominik Inauen; Govind Menon

doi:10.1214/23-ECP540

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Home > Journals > Electron. Commun. Probab. > Volume 28 > Article

2023 Motion by mean curvature and Dyson Brownian Motion

Ching-Peng Huang, Dominik Inauen, Govind Menon

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Ching-Peng Huang,¹ Dominik Inauen,² Govind Menon¹
¹Division of Applied Mathematics, Brown University, 182 George St., Providence, RI 02912
²Institut für mathematik, Universität Leipzig, D-04109, Leipzig, Germany

Electron. Commun. Probab. 28: 1-10 (2023). DOI: 10.1214/23-ECP540

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Abstract

We construct Dyson Brownian motion for $β \in (0, \infty]$ 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 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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Supported by the National Science Foundation (DMS 2107205).

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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

Information

Received: 26 January 2023; Accepted: 29 July 2023; Published: 2023

First available in Project Euclid: 5 September 2023

arXiv: 2210.11347

MathSciNet: MR4651159

Digital Object Identifier: 10.1214/23-ECP540

Subjects:

Primary: 15B51 , 53E10 , 60D05

Keywords: Dyson Brownian motion , mean curvature , Riemannian submersion

Rights: Creative Commons Attribution 4.0 International License.

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Electron. Commun. Probab.

Vol.28 • 2023

Institute of Mathematical Statistics and Bernoulli Society

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Ching-Peng Huang, Dominik Inauen, Govind Menon "Motion by mean curvature and Dyson Brownian Motion," Electronic Communications in Probability, Electron. Commun. Probab. 28(none), 1-10, (2023)

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