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arXiv · 1906.10856

Quaternionic Brownian windings

Fabrice Baudoin·Nizar Demni·Jing Wang
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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.

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Fabrice Baudoin, Nizar Demni, Jing Wang. 2019-06-26. Quaternionic Brownian windings. https://arxiv.org/abs/1906.10856

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