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- W1980156396 abstract "Given a density function f on a compact subset of Rd we look at the problem of finding the best approximation of f by discrete measures ν=∑ciδxi in the sense of the p-Wasserstein distance, subject to size constraints of the form ∑h(ci)⩽α where h is a given weight function. This is an important problem with applications in economic planning of locations and in information theory. The efficiency of the approximation can be measured by studying the rate at which the minimal distance tends to zero as α tends to infinity. In this paper, we introduce a rescaled distance which depends on a small parameter and establish a representation formula for its limit as a function of the local statistics for the distribution of the ciʼs. This allows to treat the asymptotic problem as α→∞ for a quite large class of weight functions h. Etant donnée une densité à support compact f sur Rd, on cherche la meilleure approximation de f par des mesures discrètes ν=∑ciδxi au sens de la distance de Wasserstein dʼordre p, sous une contrainte du type ∑h(ci)⩽α, où h est une fonction de poids donnée. Cʼest un problème important que lʼon rencontre notamment dans le domaine de lʼéconomie urbaine et en théorie de lʼinformation. Lʼefficacité de lʼapproximation peut être mesurée en étudiant à quelle vitesse la distance minimale tend vers zéro quand α tend vers lʼinfini. Dans cet article on introduit une distance normalisée dépendant dʼun petit paramètre et on établit une formule de représentation pour sa limite en fonction de la statistique locale de distribution des coefficients ci. On peut ainsi traiter le problème asymptotique α→∞ pour une très large classe de fonctions h." @default.
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- W1980156396 date "2011-04-01" @default.
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- W1980156396 title "Asymptotic analysis of a class of optimal location problems" @default.
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- W1980156396 doi "https://doi.org/10.1016/j.matpur.2010.10.009" @default.
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