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Extremal measures maximizing functionals based on simplicial volumes

Abstract : We consider functionals measuring the dispersion of a d-dimensional distribution which are based on the volumes of simplices of dimension k ≤ d formed by k + 1 independent copies and raised to some power δ. We study properties of extremal measures that maximize these functionals. In particular, for positive δ we characterize their support and for negative δ we establish connection with potential theory and motivate the application to space-filling design for computer experiments. Several illustrative examples are presented.
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Submitted on : Wednesday, April 27, 2016 - 11:29:50 AM
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Luc Pronzato, Henry Wynn, Anatoly Zhigljavsky. Extremal measures maximizing functionals based on simplicial volumes. Statistical Papers, Springer Verlag, 2016, 57 (4), pp.1059-1075. ⟨10.1007/s00362-016-0767-6⟩. ⟨hal-01308116⟩

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