The expected volume of a random polytope in a ball
For any convex body K in d‐dimensional Euclidean space Ed(d≥2) and for integers n and i, n ≥ d + 1,1 ≤ i ≤ n, let V(d) n‐ii(K) be the expected volume of the convex hull Hn‐i, i of n independent random points, of which n‐i are uniformly distributed in the interior, the other i on the boundary of K. W...
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| Formato: | Capítulo de libro |
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1988
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 07320caa a22007697a 4500 | ||
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| 003 | AR-BaUEN | ||
| 005 | 20230518204922.0 | ||
| 008 | 190411s1988 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84986656862 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Affentranger, F. | |
| 245 | 1 | 4 | |a The expected volume of a random polytope in a ball |
| 260 | |c 1988 | ||
| 270 | 1 | 0 | |m Affentranger, F.; Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428, Argentina |
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Baddeley, A., Integrals on a moving manifold and geometrical probability (1977) Advances in Applied Probability, 9, pp. 588-603 | ||
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| 504 | |a Blaschke, W., (1923) Vorlesungen über Differentialgeometrie II., , Springer, Berlin | ||
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| 504 | |a Buchta, C., Stochastische Approximation konvexer Polygone (1984) Z. Wahrsch. verw. Geb., 67, pp. 283-304 | ||
| 504 | |a Buchta, C., Zufällige Polyeder—Eine Uebersicht. In: Zahlentheoretische Analysis (ed. by E. Hlawka) (1985) Lect. Notes Math., 1114, pp. 1-13. , Springer, Berlin | ||
| 504 | |a Buchta, C., A note on the volume of a random polytope in a tetrahedron (1986) Illinois J. Math., 30, pp. 653-659 | ||
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| 504 | |a Santaló, L.A., (1976) Integral Geometry and Geometric Probability., , Addison‐Wesley, Reading, MA | ||
| 504 | |a Schneider, R., Random approximation of convex sets (1988) Proceedings of the Fourth International Conference in Stereology and Stochastic Geometry. J. Microsc., 151, pp. 211-227 | ||
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| 504 | |a Woolhouse, W., (1867) Educational Times | ||
| 520 | 3 | |a For any convex body K in d‐dimensional Euclidean space Ed(d≥2) and for integers n and i, n ≥ d + 1,1 ≤ i ≤ n, let V(d) n‐ii(K) be the expected volume of the convex hull Hn‐i, i of n independent random points, of which n‐i are uniformly distributed in the interior, the other i on the boundary of K. We develop an integral formula for V(d) n‐i, i(K) for the case that K is a d‐dimensional unit ball by considering an adequate decomposition of V(d) n‐i, i into d‐dimensional simplices. To solve the important case i = 0, that is the case in which all points are chosen at random from the interior of Bd, we require in addition Crofton's theorem on mean values. We illustrate the usefulness of our results by treating some special cases and by giving numerical values for the planar and the three‐dimensional cases. 1988 Blackwell Science Ltd |l eng | |
| 593 | |a Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, 1428, Argentina | ||
| 690 | 1 | 0 | |a CROFTON'S THEOREM ON MEAN VALUES |
| 690 | 1 | 0 | |a EXPECTED VOLUME OF A RANDOM POLYTOPE |
| 690 | 1 | 0 | |a GEOMETRIC PROBABILITIES |
| 690 | 1 | 0 | |a INSCRIBED RANDOM POLYTOPES |
| 690 | 1 | 0 | |a INTEGRAL GEOMETRY |
| 690 | 1 | 0 | |a SET OF UNIFORM RANDOM POINTS |
| 690 | 1 | 0 | |a STOCHASTIC GEOMETRY |
| 690 | 1 | 0 | |a SYLVESTER'S PROBLEM |
| 773 | 0 | |d 1988 |g v. 151 |h pp. 277-287 |k n. 3 |p J. Microsc. |x 00222720 |w (AR-BaUEN)CENRE-925 |t Journal of Microscopy | |
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| 856 | 4 | 0 | |u https://doi.org/10.1111/j.1365-2818.1988.tb04688.x |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00222720_v151_n3_p277_Affentranger |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222720_v151_n3_p277_Affentranger |y Registro en la Biblioteca Digital |
| 961 | |a paper_00222720_v151_n3_p277_Affentranger |b paper |c PE | ||
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| 999 | |c 78960 | ||