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Statistical Papers

, Volume 57, Issue 4, pp 1059–1075 | Cite as

Extremal measures maximizing functionals based on simplicial volumes

  • Luc Pronzato
  • Henry P. Wynn
  • Anatoly Zhigljavsky
Regular Article

Abstract

We consider functionals measuring the dispersion of a d-dimensional distribution which are based on the volumes of simplices of dimension \(k\le d\) formed by \(k+1\) independent copies and raised to some power \(\delta \). We study properties of extremal measures that maximize these functionals. In particular, for positive \(\delta \) we characterize their support and for negative \(\delta \) we establish connection with potential theory and motivate the application to space-filling design for computer experiments. Several illustrative examples are presented.

Keywords

Potential theory Logarithmic potential Computer experiments Space-filling design 

Mathematics Subject Classification

62K05 31C15 

Notes

Acknowledgments

The work of the first author was partly supported by the ANR project 2011-IS01-001-01 DESIRE (DESIgns for spatial Random fiElds). The third author was supported by the Russian Science Foundation, project Nb. 15-11-30022 “Global optimization, supercomputing computations, and application”.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Luc Pronzato
    • 1
  • Henry P. Wynn
    • 2
  • Anatoly Zhigljavsky
    • 3
    • 4
  1. 1.CNRS, Laboratoire I3S, UMR 7172, UNS, CNRS; 2000route des Lucioles, Les Algorithmes, bât. Euclide BSophia AntipolisFrance
  2. 2.London School of EconomicsLondonUK
  3. 3.School of MathematicsCardiff UniversityCardiffUK
  4. 4.Lobachevsky Nizhny Novgorod State UniversityNizhny NovgorodRussia

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