The Experts below are selected from a list of 7401 Experts worldwide ranked by ideXlab platform
Viktor Vigh - One of the best experts on this subject based on the ideXlab platform.
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intrinsic volumes of inscribed random polytopes in smooth convex bodies
Advances in Applied Probability, 2010Co-Authors: Imre Barany, Ferenc Fodor, Viktor VighAbstract:Let K be a d-dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by K-n the convex hull of n points chosen randomly and independently from K according to the uniform distribution. Matching lower and upper bounds are obtained for the orders of magnitude of the variances of the sib intrinsic volumes V-s(K-n) of K-n for s is an element of {1, ... , d}. Furthermore, strong laws of large numbers are proved for the intrinsic volumes of K-n. The essential tools are the economic cap Covering Theorem of Barany and Larman, and the Efron-Stein jackknife inequality.
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intrinsic volumes of inscribed random polytopes in smooth convex bodies
arXiv: Metric Geometry, 2009Co-Authors: Imre Barany, Ferenc Fodor, Viktor VighAbstract:Let $K$ be a $d$ dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by $K_n$ the convex hull of $n$ points chosen randomly and independently from $K$ according to the uniform distribution. Matching lower and upper bounds are obtained for the orders of magnitude of the variances of the $s$-th intrinsic volumes $V_s(K_n)$ of $K_n$ for $s\in\{1, ..., d\}$. Furthermore, strong laws of large numbers are proved for the intrinsic volumes of $K_n$. The essential tools are the Economic Cap Covering Theorem of B\'ar\'any and Larman, and the Efron-Stein jackknife inequality.
Arno Pauly - One of the best experts on this subject based on the ideXlab platform.
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the vitali Covering Theorem in the weihrauch lattice
Lecture Notes in Computer Science, 2017Co-Authors: Vasco Brattka, Guido Gherardi, Rupert Holzl, Arno PaulyAbstract:We study the uniform computational content of the Vitali Covering Theorem for intervals using the tool of Weihrauch reducibility. We show that a more detailed picture emerges than what a related study by Giusto, Brown, and Simpson has revealed in the setting of reverse mathematics. In particular, different formulations of the Vitali Covering Theorem turn out to have different uniform computational content. These versions are either computable or closely related to uniform variants of Weak Weak Kőnig’s Lemma.
Imre Barany - One of the best experts on this subject based on the ideXlab platform.
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intrinsic volumes of inscribed random polytopes in smooth convex bodies
Advances in Applied Probability, 2010Co-Authors: Imre Barany, Ferenc Fodor, Viktor VighAbstract:Let K be a d-dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by K-n the convex hull of n points chosen randomly and independently from K according to the uniform distribution. Matching lower and upper bounds are obtained for the orders of magnitude of the variances of the sib intrinsic volumes V-s(K-n) of K-n for s is an element of {1, ... , d}. Furthermore, strong laws of large numbers are proved for the intrinsic volumes of K-n. The essential tools are the economic cap Covering Theorem of Barany and Larman, and the Efron-Stein jackknife inequality.
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intrinsic volumes of inscribed random polytopes in smooth convex bodies
arXiv: Metric Geometry, 2009Co-Authors: Imre Barany, Ferenc Fodor, Viktor VighAbstract:Let $K$ be a $d$ dimensional convex body with a twice continuously differentiable boundary and everywhere positive Gauss-Kronecker curvature. Denote by $K_n$ the convex hull of $n$ points chosen randomly and independently from $K$ according to the uniform distribution. Matching lower and upper bounds are obtained for the orders of magnitude of the variances of the $s$-th intrinsic volumes $V_s(K_n)$ of $K_n$ for $s\in\{1, ..., d\}$. Furthermore, strong laws of large numbers are proved for the intrinsic volumes of $K_n$. The essential tools are the Economic Cap Covering Theorem of B\'ar\'any and Larman, and the Efron-Stein jackknife inequality.
Vasco Brattka - One of the best experts on this subject based on the ideXlab platform.
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the vitali Covering Theorem in the weihrauch lattice
Lecture Notes in Computer Science, 2017Co-Authors: Vasco Brattka, Guido Gherardi, Rupert Holzl, Arno PaulyAbstract:We study the uniform computational content of the Vitali Covering Theorem for intervals using the tool of Weihrauch reducibility. We show that a more detailed picture emerges than what a related study by Giusto, Brown, and Simpson has revealed in the setting of reverse mathematics. In particular, different formulations of the Vitali Covering Theorem turn out to have different uniform computational content. These versions are either computable or closely related to uniform variants of Weak Weak Kőnig’s Lemma.
Anton Hedin - One of the best experts on this subject based on the ideXlab platform.
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1 The Vitali Covering Theorem in constructive mathematics HANNES DIENER
2015Co-Authors: Anton HedinAbstract:Abstract: This paper investigates the Vitali Covering Theorem from various constructive angles. A Vitali Cover of a metric space is a cover such that for every point there exists an arbitrarily small element of the cover containing this point. The Vitali Covering Theorem now states, that for any Vitali Cover one can find a finite family of pairwise disjoint sets in the Vitali Cover that cover the entire space up to a set of a given non-zero measure. We will show, by means of a recursive counterexample, that there cannot be a fully constructive proof, but that adding a very weak semi-constructive principle suffices to give such a proof. Lastly, we will show that with an appropriate formalization in formal topology the non-constructive problems can be avoided completely
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the vitali Covering Theorem in constructive mathematics
Journal of Logic and Analysis, 2012Co-Authors: H C Diener, Anton HedinAbstract:This paper investigates the Vitali Covering Theorem from various constructive angles. A Vitali Cover of a metric space is a cover such that for every point there exists an arbitrarily small set of ...
