Abstract
We define and study the three-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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Author supported in part by the Simons Foundation and NSF Grant DMS-1901315.
Author supported by the NSF Grant DMS-1855523.
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Baudoin, F., Demni, N. & Wang, J. Quaternionic Brownian Windings. J Theor Probab 34, 2368–2385 (2021). https://doi.org/10.1007/s10959-020-01034-9
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DOI: https://doi.org/10.1007/s10959-020-01034-9
Keywords
- Stochastic winding
- Large time asymptotic
- Quaternionic projective space
- Quaternionic hyperbolic space
- Cauchy relativistic distribution