Skip to main content
SpringerLink
Log in

Random Sections of Spherical Convex Bodies

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Let K ⊂ 𝕊d−1 be a convex spherical body. Denote by Δ(K) the distance between two random points in K and denote by σ(K) the length of a random chord of K. The distribution of Δ(K) is explicitly expressed via the distribution of σ(K). This enables one to find the density of the distribution of Δ(K), where K is a spherical cap.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Aharonyan and V. Ohanyan, “Moments of the distance between two random points,” Model. Artif. Intell., 10, No. 2, 64–70 (2016).

    Google Scholar 

  2. E. Arbeiter and M. Zähle, “Kinematic relations for Hausdorff moment measures in spherical spaces,” Math. Nachr., 153, 333–348 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  3. G. D. Chakerian, “Inequalities for the difference body of a convex body,” Proc. Amer. Math. Soc., 18, 879–884 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Crofton, “Probability,” in: Encyclopedia Britannica Inc, 9th ed. (1885), pp. 758–788.

  5. H. Hadwiger, “Ueber zwei quadratische Distanzintegrale für Eikörper,” Arch. Math., 3, 142–144 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  6. J. F. C. Kingman, “Random secants of a convex body,” J. Appl. Probability, 6, 660–672 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Moseeva, “Random sections of convex bodies,” Zap. Nauchn. Semin. POMI, 486, 190–199 (2019).

    MathSciNet  MATH  Google Scholar 

  8. R. Schneider and W. Weil, Stochastic and Integral Geometry, Springer-Verlag, Berlin (2008).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Leonhard Euler International Mathematical Institute, St Petersburg, Russia

    T. Moseeva

  2. St. Petersburg State University, St. Petersburg, Russia

    A. Tarasov

  3. St. Petersburg Department of the Steklov Institute of Mathematics, St. Petersburg, Russia

    D. Zaporozhets

Authors
  1. T. Moseeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Tarasov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Zaporozhets
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Moseeva.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 495, 2020, pp. 198–208.

Translated by the authors.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moseeva, T., Tarasov, A. & Zaporozhets, D. Random Sections of Spherical Convex Bodies. J Math Sci 268, 656–662 (2022). https://doi.org/10.1007/s10958-022-06236-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-022-06236-6

Search

Navigation