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arXiv · 2006.02186

Convex bodies generated by sublinear expectations of random vectors

Ilya Molchanov·Riccardo Turin
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Abstract

We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random vectors in Euclidean space. We identify the dual representation of such convex bodies and describe a construction that serves as a building block for all so defined convex bodies.

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Ilya Molchanov, Riccardo Turin. 2020-06-03. Convex bodies generated by sublinear expectations of random vectors. https://arxiv.org/abs/2006.02186

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