Floating bodies and random polytopes

Abstract: I will present some results about the geometry of centrally-symmetric random polytopes, generated by $N$ independent copies of a random vector $X$ taking values in $\R^n$. Under minimal assumptions on $X$, for $N \gtrsim n$ and with high probability, the polytope contains a deterministic set that is naturally associated with the random vector---namely, the polar of a certain floating body. This solves the long-standing question on whether such a random polytope contains a canonical body. This is joint work with F. Krahmer, C. Kummerle, S. Mendelson and H; Rauhut.

analysis of PDEsmetric geometry

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

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