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Random polytopes and phenomena in high dimensions

Symposium
Thursday, 7 April, 2016, at 13:15-14:00, in Koll. D (1531-211)
Christoph Thäle (Ruhr-Universität Bochum)
Abstract:

Random polytopes in $\mathbb{R}^n$ arise by taking the convex hull of a finite number of random points that are distributed according to some fixed probability distribution (for example, the uniform distribution on a convex body or the standard Gaussian distribution). Alternatively, random polytopes can also be generated as intersection of random half-spaces, and, in particular, as cells of a random tessellation of $\mathbb{R}^n$. We present results that pertain the geometry of such random polytopes in high dimensions, that is, as $n\to\infty$. In particular, we review their connection to the hyperplane or slicing conjecture, one of the major open problems in asymptotic geometric analysis. 

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Revised 03.01.2017