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  • 1 Alfréd Rényi Institute of Mathematics H-1364 Budapest P. O. Box: 127 Hungary
  • | 2 Technische Universität Wien Institut für Diskrete Mathematik und Geometrie Wiedner Hauptstr. 8-10 A-1040 Wien Austria
  • | 3 Universität Karlsruhe (TH), KIT Institut für Algebra und Geometrie D-76133 Karlsruhe Germany
  • | 4 Eötvös Loránd University Department of Geometry Pázmány Péter sétány 1/C H-1117 Budapest Hungary
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Abstract  

Let K be a convex body in ℝd, let j ∈ {1, …, d−1}, and let K(n) be the convex hull of n points chosen randomly, independently and uniformly from K. If ∂K is C + 2, then an asymptotic formula is known due to M. Reitzner (and due to I. Bárány if ∂K is C + 3) for the difference of the jth intrinsic volume of K and the expectation of the jth intrinsic volume of K(n). We extend this formula to the case when the only condition on K is that a ball rolls freely inside K.

Manuscript Submission: HERE

  • Impact Factor (2019): 0.693
  • Scimago Journal Rank (2019): 0.412
  • SJR Hirsch-Index (2019): 20
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.664
  • Scimago Journal Rank (2018): 0.412
  • SJR Hirsch-Index (2018): 19
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1971
Volumes
per Year
2
Issues
per Year
4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address
H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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