Asymptotic of an optimal location problem. (Asymptotique d’un problème de positionnement optimal.) (French. Abridged English version) Zbl 1041.90025

Bouchitté, Guy; Jimenez, Chloé; Rajesh, Mahadevan

C. R., Math., Acad. Sci. Paris 335, No. 10, 853-858 (2002).

It is known that for a uniform demand density on the unit \(d\)-cube the minimum mean distance to the closest of \(n\) points, asymptotically equals \(C_dn^{-1/d}\). In particular \(C_2\) is known to be the average distance to the center for a uniform hexagon of unit area. In this paper the asymptotic result is extended to non uniform unit density \(f\), yielding the same value multiplied by \((\int f^p(x)\,dx)^{1/p}\) with \(p=d/(d+1)\).

Reviewer: Frank Plastria (Brussels)

MSC:

90B85	Continuous location
91B72	Spatial models in economics
49J45	Methods involving semicontinuity and convergence; relaxation

Keywords:

Mass transportation; Wasserstein distance; \(\Gamma\)-convergence

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