Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 58: Issue 4
Another Look at Threshold Phenomena for Random Cones
Authors:
Daniel Hug Karlsruhe Institute of Technology (KIT), Department of Mathematics, D-76128 Karlsruhe, Germany

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and
Rolf Schneider Mathematisches Institut, Albert-Ludwigs-Universität, D-79104 Freiburg i. Br., Germany

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Pages:
489–504
Online Publication Date:
21 Oct 2021
Publication Date:
03 Dec 2021
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2021.01513
Keywords:
Cover–Efron cone; face numbers; high dimensions; threshold phenomenon
Restricted access

In stochastic geometry there are several instances of threshold phenomena in high dimensions: the behavior of a limit of some expectation changes abruptly when some parameter passes through a critical value. This note continues the investigation of the expected face numbers of polyhedral random cones, when the dimension of the ambient space increases to infinity. In the focus are the critical values of the observed threshold phenomena, as well as threshold phenomena for differences instead of quotients.

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    T. M. Cover and B. Efron. Geometrical probability and random points on a hypersphere. Ann. Math. Stat., 38:213–220, 1967.

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    O. Devillers, M. Glisse, X. Goaoc, G. Moroz and M. Reitzner. The monotonicity of f-vectors of random polytopes. Electron. Commun. Probab., 18(23):8 pp, 2013.

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    D. L. Donoho and J. Tanner. Counting the faces of randomly-projected hypercubes and orthants, with applications. Discrete Comput. Geom., 43:522–541, 2010.

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    T. Godland, Z. Kabluchko and C. Thäle. Random cones in high dimensions I: Donoho– Tanner and Cover–Efron cones. arXiv:2012.06189v1

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    D. Hug and R. Schneider. Random conical tessellations. Discrete Comput. Geom., 56:395–426, 2016.

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    D. Hug and R. Schneider. Threshold phenomena for random cones. Discrete Comput. Geom., accepted. arXiv:2004.11473v2.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

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

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Gábor SÁGI (Rényi Institute of Mathematics)

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  • 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")

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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)

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