Quaternionic Brownian windings
Probability
2019-06-27 v1
Abstract
We define and study the 3-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic 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. The corresponding asymptotic law seems to be new and is related to the Cauchy relativistic distribution.
Cite
@article{arxiv.1906.10856,
title = {Quaternionic Brownian windings},
author = {Fabrice Baudoin and Nizar Demni and Jing Wang},
journal= {arXiv preprint arXiv:1906.10856},
year = {2019}
}