Asymptotic windings of the block determinants of a unitary Brownian motion and related diffusions

2020/04/27 by Fabrice Baudoin, Jing Wang, Baudoin, Fabrice +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2004.13098

openalex publication_date 2020/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Generalized stochastic areas, Winding numbers, and hyperbolic Stiefel fibrations
• Brownian motion and stochastic areas on complex partial flag manifolds with blocks of equal size
• Schur-Weyl duality and the Product of randomly-rotated symmetries by a unitary Brownian motion
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• Stochastic areas, Winding numbers and Hopf fibrations