The combinatorial structure of random polytopes

By Matthias Reitzner. 2005

76 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/a9e7e3b5cfe2d3a892d3dadf81b01fa22a3b1e02

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In Applied Mathematics

In Computer Graphics and Computer-Aided Design

In Discrete Mathematics and Combinatorics

Citations in the corpus

Random points and lattice points in convex bodies (2008, methodology): “Then Km is equal to Πn|N = m. Reitzner proved the central limit theorem for Vol Πn and fj(Πn), a remarkable achievement, in the following form.”
General affine surface areas (2009, background): “Since many basic problems in discrete and stochastic geometry are equi-affine invariant, equi-affine surface area has found numerous applications in these fields (see, for example, [3], [4], [11], [35]).”
A classification of $\operatorname{SL}(n)$ invariant valuations (2010, background): “In addition, since many basic problems in discrete and stochastic geometry are equi-affine invariant, affine surface area has found numerous applications in these fields (see, for example, [11], [12], [18], [50]).”
Centro-Affine Invariants for Smooth Convex Bodies (2010, background): “2 ALINA STANCU1 to be an invaluable tool in convexity (see the monograph [21]), stochastic geometry, [4], [9] – [12], [41], differential geometry and differential equations [1], [3], [42], [49] – [53].”
Central limit theorems for random polytopes (2005, background): “= O(n1− 4 d+1 ) because it follows from (27) in [22] and Theorem 6 in [21] that”
The Spherical Convex Floating Body (2014, unknown): “For instance, affine surface area appears in best and random approximation of convex bodies by polytopes, see K. Böröczky Jr. [11] [12], P. M. Gruber [26] [27] [28], M. Ludwig [38], M. Reitzner [59] and C. Schütt [68] [70].”
Expected intrinsic volumes and facet numbers of random beta‐polytopes (2017, methodology): “□ ACKNOWLEDGEMENTS We would like to thank Matthias Reitzner (Osnabrück) for making reference [10] available to us.”
Beta polytopes and Poisson polyhedra: f-vectors and angles (2018, background): “In [29] he has shown that if Kn is the convex hull of n ≥ d+ 1 uniformly distributed random points in a convex body K ⊆ Rd with twice differentiable boundary ∂K and everywhere positive Gaussian curvature κ( · ) then, for every k ∈ {0, 1, .”