Seminar Mathematics - Dr. G. Bonnet

Title: High Dimensional Random Polytopes

Abstract:
In the first part of our talk we give a general overview of Stochastic Geometry. In the second part we consider the convex hull Pn,d of n>d +1 i.i.d. random points in Rd where the points are distributed with respect to some classical family of distributions such as the uniform distribution in the unit ball or on its boundary. We study its facets' distribution as well as classical functionals of this random polytope such as its (intrinsic) volume(s). We are going to present high dimensional asymptotic results within this context. This talk is based on the following articles:

• Threshold phenomena for high-dimensional random polytopes, joint work with G. Chasapis, J. Grote, D. Temesvari and N. Turchi, Communications in Comtemporary Mathematics, Vol. 21, No. 05, (2019) ;
• Facets of spherical random polytopes, joint work with E. O'Reilly, arXiv:1908.04033 ;
• Phase transition of the volume of beta-polytopes, joint work with N. Turchi and Z. Kabluchko, arXiv:1911.12696.

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