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arXiv · 2007.07297

Random sections of spherical convex bodies

Tatiana Moseeva·Alexander Tarasov·Dmitry Zaporozhets
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Abstract

Let $K\subset\mathbb S^{d-1}$ be a convex spherical body. Denote by $\Delta(K)$ the distance between two random points in $K$ and denote by $\sigma(K)$ the length of a random chord of $K$. We explicitly express the distribution of $\Delta(K)$ via the distribution of $\sigma(K)$. From this we find the density of distribution of $\Delta(K)$ when $K$ is a spherical cap.

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Tatiana Moseeva, Alexander Tarasov, Dmitry Zaporozhets. 2020-07-14. Random sections of spherical convex bodies. https://arxiv.org/abs/2007.07297

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