Random Polytopes with Vertices on the Boundary of a Ball or a Cube

Onstwedder, Marit (2022) Random Polytopes with Vertices on the Boundary of a Ball or a Cube. Master's Thesis / Essay, Mathematics.

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Abstract

Let X_1,...,X_N be independent points that are uniformly distributed on the boundary of a compact convex set P and let P_N be the convex hull of those points. This thesis gives an extensive proof of the following two (already existing) theorems. If P=B^d, which is the d-dimensional unit ball, then E[V_d(B^d)-V_d(P_N)] = O(N^(-2/(d-1))) as N goes to infinity. If P=C:=[0,1]^3, then the expected number of facets of the convex hull P_N is E[f_2(P_N)] = c ln N (1+O((ln N)^(-1))) as N goes to infinity, with some c>0 independent of C.

Item Type:	Thesis (Master's Thesis / Essay)
Supervisor name:	Bonnet, G.F.Y. and Muller, T.
Degree programme:	Mathematics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	15 Jul 2022 12:40
Last Modified:	15 Jul 2022 12:40
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/27865

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