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2021 Asymptotic windings of the block determinants of a unitary Brownian motion and related diffusions
Fabrice Baudoin, Jing Wang
Author Affiliations +
Electron. J. Probab. 26: 1-21 (2021). DOI: 10.1214/21-EJP600

Abstract

We study several matrix diffusion processes constructed from a unitary Brownian motion. In particular, we use the Stiefel fibration to lift the Brownian motion of the complex Grassmannian to the complex Stiefel manifold and deduce a skew-product decomposition of the Stiefel Brownian motion. As an application, we prove asymptotic laws for the determinants of the block entries of the unitary Brownian motion.

Funding Statement

F.B. was partly supported by the NSF grant DMS 1901315. J.W. was partly supported by the NSF grant DMS 1855523.

Citation

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Fabrice Baudoin. Jing Wang. "Asymptotic windings of the block determinants of a unitary Brownian motion and related diffusions." Electron. J. Probab. 26 1 - 21, 2021. https://doi.org/10.1214/21-EJP600

Information

Received: 1 October 2020; Accepted: 3 March 2021; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1214/21-EJP600

Subjects:
Primary: 60B20, 60J35, 60J60

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Vol.26 • 2021
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