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