Authors:
Kinga Nagy Department of Geometry, Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary

Search for other papers by Kinga Nagy in
Current site
Google Scholar
PubMed
Close
and
Viktor Vígh Department of Geometry, Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary

Search for other papers by Viktor Vígh in
Current site
Google Scholar
PubMed
Close
Restricted access

In this paper, we consider the asymptotic behaviour of the expectation of the number of vertices of a uniform random spherical disc-polygon. This provides a connection between the corresponding results in spherical convexity, and in Euclidean spindle-convexity, where the expectation tends to the same constant. We also extend the result to a more general case, where the random points generating the uniform random disc-polygon are chosen from spherical convex disc with smooth boundary.

  • [1]

    E. Artin. The gamma function. Holt, Rinehart and Winston, 1964.

  • [2]

    I. Bárány. Random points and lattice points in convex bodies. Bulletin of the American Mathematical Society, 45(3):339365, 2007.

  • [3]

    I. Bárány, D. Hug, M. Reitzner, and R. Schneider. Random points in halfspheres. Random Struct. Alg., 50:322, 2017.

  • [4]

    F. Besau, A. Gusakova, M. Reitzner, C. Schütt, C. Thäle, and E. Werner. Spherical convex hull of random points on a wedge. Math. Ann., 389(3):22892316, 2023.

    • Search Google Scholar
    • Export Citation
  • [5]

    K. Bezdek, Z. Lángi, M. Naszódi, and P. Papez. Ball-polyhedra, Discrete Comput. Geom., 38(2):201230, 2007.

  • [6]

    K. J. Böröczky, F. Fodor, M. Reitzner, and V. Vígh. Mean width of inscribed random polytopes in a reasonably smooth convex body. J. Multivariate Anal., 100:22872295, 2009.

    • Search Google Scholar
    • Export Citation
  • [7]

    B. Csikós. On the Volume of Flowers in Space Forms, Geometriae Dedicata, 86:5979, 2001.

  • [8]

    F. Fodor. Random ball-polytopes in smooth convex bodies. arXiv: 1906.11480v1, 2020.

  • [9]

    F. Fodor, P. Kevei, and V. Vígh. On random disc polygons in smooth convex discs, Adv. in Appl. Probab., 46(4):899918, 2014.

  • [10]

    F. Fodor, P. Kevei, and V. Vígh. On random disc polygons in a disc-polygon. Electron. Commun. Probab., 28:111, 2023.

  • [11]

    H. Martini, L. Montejano, and D. Oliveros. Bodies of Constant Width. Birkhäuser, 2019.

  • [12]

    R. Schneider, and W. Weil. Stochastic and Integral Geometry. Probability and Its Applications. Springer, 2008.

  • [13]

    A. Rényi and R. Sulanke. Über die konvexe Hülle von 𝑛 zufällig gewählten Punkten. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 2:7584, 1963.

    • Search Google Scholar
    • Export Citation
  • Collapse
  • Expand

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu

Indexing and Abstracting Services:

  • CABELLS Journalytics
  • CompuMath Citation Index
  • Essential Science Indicators
  • Mathematical Reviews
  • Science Citation Index Expanded (SciSearch)
  • SCOPUS
  • Zentralblatt MATH

2023  
Web of Science  
Journal Impact Factor 0.4
Rank by Impact Factor Q4 (Mathematics)
Journal Citation Indicator 0.49
Scopus  
CiteScore 1.3
CiteScore rank Q2 (General Mathematics)
SNIP 0.705
Scimago  
SJR index 0.239
SJR Q rank Q3

Studia Scientiarum Mathematicarum Hungarica
Publication Model Hybrid
Submission Fee none
Article Processing Charge 900 EUR/article (only for OA publications)
Printed Color Illustrations 40 EUR (or 10 000 HUF) + VAT / piece
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription fee 2025 Online subsscription: 796 EUR / 876 USD
Print + online subscription: 900 EUR / 988 USD
Subscription Information Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content.
Purchase per Title Individual articles are sold on the displayed price.

Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation
1966
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)