Deviation inequalities for random polytopes in arbitrary convex bodies

Bernoulli ◽  
2020 ◽  
Vol 26 (4) ◽  
pp. 2488-2502
Author(s):  
Victor-Emmanuel Brunel
Keyword(s):  
Convex Bodies ◽  
Random Polytopes ◽  
Arbitrary Convex ◽  
Deviation Inequalities

Random polytopes in isotropic convex bodies

2014 ◽  
pp. 357-388 ◽  
Author(s):  
Silouanos Brazitikos ◽  
Apostolos Giannopoulos ◽  
Petros Valettas ◽  
Beatrice-Helen Vritsiou
Keyword(s):  
Convex Bodies ◽  
Random Polytopes

scholarly journals Variance asymptotics for random polytopes in smooth convex bodies

2013 ◽  
Vol 158 (1-2) ◽  
pp. 435-463 ◽  
Author(s):  
Pierre Calka ◽  
J. E. Yukich
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Random Polytopes

scholarly journals Random polytopes and the volume-product of symmetric convex bodies.

1985 ◽  
Vol 57 ◽  
pp. 386 ◽  
Author(s):  
Shlomo Reisner
Keyword(s):  
Convex Bodies ◽  
Symmetric Convex ◽  
Random Polytopes ◽  
Volume Product

Approximation of convex bodies by random polytopes

1987 ◽  
Vol 32 (1) ◽  
pp. 304-310 ◽  
Author(s):  
Rolf Schneider
Keyword(s):  
Convex Bodies ◽  
Random Polytopes ◽  
Approximation Of Convex Bodies

On determinants and the volume of random polytopes in isotropic convex bodies

2010 ◽  
Vol 149 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Peter Pivovarov
Keyword(s):  
Convex Bodies ◽  
Random Polytopes

scholarly journals Approximation of smooth convex bodies by random polytopes

2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Julian Grote ◽  
Elisabeth Werner
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Random Polytopes

scholarly journals Random Inscribing Polytopes

2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Ross M. Richardson ◽  
Van H. Vu ◽  
Lei Wu
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Poisson Process ◽  
Central Limit ◽  
Convex Bodies ◽  
Higher Moments ◽  
Random Polytopes ◽  
International Audience

International audience For convex bodies $K$ with $\mathcal{C}^2$ boundary in $\mathbb{R}^d$, we provide results on the volume of random polytopes with vertices chosen along the boundary of $K$ which we call $\textit{random inscribing polytopes}$. In particular, we prove results concerning the variance and higher moments of the volume, as well as show that the random inscribing polytopes generated by the Poisson process satisfy central limit theorem.

scholarly journals Convex bodies, economic cap coverings, random polytopes

Mathematika ◽  
1988 ◽  
Vol 35 (2) ◽  
pp. 274-291 ◽  
Author(s):  
I. Bárány ◽  
D. G. Larman
Keyword(s):  
Convex Bodies ◽  
Random Polytopes

scholarly journals Random polytopes in smooth convex bodies

Mathematika ◽  
1992 ◽  
Vol 39 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Imre Bárány
Keyword(s):  
Convex Bodies ◽  
Smooth Convex ◽  
Random Polytopes
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