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

被引：5

作者：

Baudoin, Fabrice ^{[1
]}

Wang, Jing ^{[2
]}

机构：

[1] Univ Connecticut, Storrs, CT 06269 USA

[2] Purdue Univ, W Lafayette, IN 47907 USA

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2021年 / 26卷

关键词：

asymptotic windings; asymptotic stochastic area; block determinants; Stiefel Brownian motion; Brownian motion of complex Grassmannian manifold; GEOMETRY;

D O I：

10.1214/21-EJP600

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页数：21

共 30 条

[1]

[Anonymous], 2007, ALEA-Lat. Am. J. Prob. Math. Stat

[2]

Assiotis Theodoros, 2016, ARXIV160707182

[3] SUB-RIEMANNIAN GEOMETRY OF STIEFEL MANIFOLDS [J].