Octonionic Brownian Windings
arXiv:2008.10116
Abstract
We define and study the windings along Brownian paths in the octonionic Euclidean, projective and hyperbolic spaces which are isometric to 8-dimensional Riemannian model spaces. In particular, the asymptotic laws of these windings are shown to be Gaussian for the flat and spherical geometries while the hyperbolic winding exhibits a different long time-behavior.
To appear in Journal of Theoretical Probability