The Euclidean matching problem

We study the matching problem in finite dimensions. The Euclidean correlations of the distances can be taken into account in a systematic way. With respect to the case of independent random distances which we have studied before, the adjonction of Euclidean triangular correlations gives rise to corrections which vanish when the dimension of space goes to infinity, and remain relatively small in any dimensions Nous etudions le probleme du couplage («matching») en dimension finie. Les correlations euclidiennes entre les distances peuvent etre prises en compte de maniere systematique. Par rapport au cas des distances aleatoires independantes que nous avions etudiees precedemment, les correlations triangulaires euclidiennes engendrent des corrections qui s'annulent dans la limite ou la dimension de l'espace tend vers l'infini, et restent relativement petites a toute dimension

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