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arXiv · 2310.09697

Harmonic Interpolation and a Brunn-Minkowski Theorem for Random Determinants

Julius Ross·David Witt Nyström
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Abstract

We describe the harmonic interpolation of convex bodies, and prove a strong form of the Brunn-Minkowski inequality and characterize its equality case. As an application we improve a theorem of Berndtsson on the volume of slices of a pseudoconvex domain. We furthermore apply this to prove subharmonicity of the expected absolute value of the determinant of a matrix of random vectors through the connection with zonoids.

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Julius Ross, David Witt Nyström. 2023-10-15. Harmonic Interpolation and a Brunn-Minkowski Theorem for Random Determinants. https://arxiv.org/abs/2310.09697

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