Extremal measures maximizing functionals based on simplicial volumes
Résumé
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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A comme partie hal-01308316 Objet présenté à une conférence Luc Pronzato. A measure of dispersion based on average exponentiated volumes, with application in experimental design. ProbaStat'2015, Slovak Academy of Sciences/Comenius University, Bratislava, Jun 2015, Smolenice, Slovakia. ⟨hal-01308316⟩