Generalized Stochastic Areas, Winding Numbers, and Hyperbolic Stiefel Fibrations

TY - JOUR

T1 - Generalized Stochastic Areas, Winding Numbers, and Hyperbolic Stiefel Fibrations

AU - Baudoin, Fabrice

AU - Demni, Nizar

AU - Wang, Jing

N1 - Publisher Copyright: © 2022 The Author(s).

PY - 2023/5/1

Y1 - 2023/5/1

N2 - We study the Brownian motion on the non-compact Grassmann manifold and some of its functionals. The key point is to realize this Brownian motion as a matrix diffusion process, use matrix stochastic calculus and take advantage of the hyperbolic Stiefel fibration to study a functional that can be understood in that setting as a generalized stochastic area process. In particular, a connection to the generalized Maass Laplacian of the complex hyperbolic space is presented and applications to the study of Brownian windings in the Lie group are then given.

AB - We study the Brownian motion on the non-compact Grassmann manifold and some of its functionals. The key point is to realize this Brownian motion as a matrix diffusion process, use matrix stochastic calculus and take advantage of the hyperbolic Stiefel fibration to study a functional that can be understood in that setting as a generalized stochastic area process. In particular, a connection to the generalized Maass Laplacian of the complex hyperbolic space is presented and applications to the study of Brownian windings in the Lie group are then given.

UR - http://www.scopus.com/inward/record.url?scp=85160961486&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnac072

DO - 10.1093/imrn/rnac072

M3 - Journal article

AN - SCOPUS:85160961486

SN - 1073-7928

VL - 2023

SP - 7925

EP - 7960

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 9

ER -