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arXiv · 2410.06824

On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations

Fabrice Baudoin·Teije Kuijper
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Abstract

We give explicit formulas and asymptotics for the distribution of the index of the Brownian loop in the following geometrical settings: the complex projective line from which two points have been removed; the complex hyperbolic line from which one point has been removed; the odd dimensional spheres from which a great hypersphere has been removed; and the complex anti-de Sitter spaces. Our analysis is based on the geometry of the Hopf and anti-de Sitter fibrations, and on the relationship between winding and area forms.

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Fabrice Baudoin, Teije Kuijper. 2024-10-09. On the law of the index of Brownian loops related to the Hopf and anti-de Sitter fibrations. https://arxiv.org/abs/2410.06824

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