Deviation inequalities for random polytopes in arbitrary convex bodies

Bernoulli ◽  
2020 ◽  
Vol 26 (4) ◽  
pp. 2488-2502
Author(s):  
Victor-Emmanuel Brunel

Author(s):  
Silouanos Brazitikos ◽  
Apostolos Giannopoulos ◽  
Petros Valettas ◽  
Beatrice-Helen Vritsiou


2013 ◽  
Vol 158 (1-2) ◽  
pp. 435-463 ◽  
Author(s):  
Pierre Calka ◽  
J. E. Yukich




1987 ◽  
Vol 32 (1) ◽  
pp. 304-310 ◽  
Author(s):  
Rolf Schneider


2010 ◽  
Vol 149 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Peter Pivovarov


2018 ◽  
Vol 23 (0) ◽  
Author(s):  
Julian Grote ◽  
Elisabeth Werner


2005 ◽  
Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽  
Author(s):  
Ross M. Richardson ◽  
Van H. Vu ◽  
Lei Wu

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.



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


Mathematika ◽  
1992 ◽  
Vol 39 (1) ◽  
pp. 81-92 ◽  
Author(s):  
Imre Bárány


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