2021/06/27 by Baudoin, Fabrice, Demni, Nizar, Wang, Jing
#Differential Geometry (math.DG) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2106.14335
We study the Brownian motion on the non-compact Grassmann manifold \fracU(n-k,k) U(n-k)U(k) 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 U(n-k,k) are then given.