Harmonic Interpolation and a Brunn-Minkowski Theorem for Random Determinants
Complex Variables
2023-10-17 v1
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.
Cite
@article{arxiv.2310.09697,
title = {Harmonic Interpolation and a Brunn-Minkowski Theorem for Random Determinants},
author = {Julius Ross and David Witt Nyström},
journal= {arXiv preprint arXiv:2310.09697},
year = {2023}
}