Convex bodies generated by sublinear expectations of random vectors

2020/06/03 by Molchanov, Ilya, Turin, Riccardo
#52A27 60D05 62G30 91G70 #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.2006.02186

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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