Abstract
We define and study windings along Brownian paths on 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 flat and spherical geometries while the hyperbolic winding exhibits different long-time behavior.
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The authors thank the anonymous referee for a careful reading and remarks that greatly improved the presentation of the paper. The second author is supported by National Science Foundation grant DMS-1901315. Both authors thank professor Fabrice Baudoin for the very helpful discussions.
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Cho, G., Yang, G. Octonionic Brownian Windings. J Theor Probab 35, 1956–1973 (2022). https://doi.org/10.1007/s10959-021-01127-z
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DOI: https://doi.org/10.1007/s10959-021-01127-z