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On the oscillation of the expected number of extreme points of a random set

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  • Devroye, Luc

Abstract

Let ENn be the expected number of extreme points among n i.i.d. points with a common radially symmetric distribution in the plane. We show that for any monotone sequence [omega]n [short up arrow] [infinity] and for every [var epsilon] > 0, there exists a radially symmetric distribution for which ENn [greater-or-equal, slanted] n/[omega]n infinitely often and ENn [less-than-or-equals, slant] 4 + [var epsilon] infinitely often. In addition, there exists a unimodal radially symmetric density such that ENn [greater-or-equal, slanted] n/[omega]n infinitely often and ENn [less-than-or-equals, slant] 4 + [var epsilon] infinitely often.

Suggested Citation

  • Devroye, Luc, 1991. "On the oscillation of the expected number of extreme points of a random set," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 281-286, April.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:4:p:281-286
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    Cited by:

    1. Ohad Navon, 2016. "Evolutionarily Stable Strategies of Random Games and the Facets of Random Polytopes," Discussion Paper Series dp702, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Sergiu Hart & Yosef Rinott & Benjamin Weiss, 2007. "Evolutionarily Stable Strategies of Random Games, and the Vertices of Random Polygons," Levine's Bibliography 321307000000000781, UCLA Department of Economics.
    3. Massé, Bruno, 1999. "On the variance of the number of extreme points of a random convex hull," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 123-130, August.

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