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Comptes Rendus Mathématique
Volume 352, n° 11
pages 935-940 (novembre 2014)
Doi : 10.1016/j.crma.2014.08.015
Received : 23 April 2014 ;  accepted : 26 August 2014
Probabilities of hitting a convex hull
Probabilités d'atteinte d'une enveloppe convexe
 

Zhenxia Liu a , Xiangfeng Yang b
a Blåeldsvägen 12B, Sturefors, Sweden 
b Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden 

Abstract

In this note, we consider the non-negative least-square method with a random matrix. This problem has connections with the probability that the origin is not in the convex hull of many random points. As related problems, suitable estimates are obtained as well on the probability that a small ball does not hit the convex hull.

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Résumé

Dans cette Note, nous appliquons la méthode des moindres carrés non négatifs d'une matrice aléatoire. Ce problème est connecté à la probabilité que l'enveloppe convexe de points aléatoires ne contienne pas l'origine. En relation avec ce problème, nous obtenons aussi des estimations de la probabilité qu'une petite boule ne rencontre pas une enveloppe convexe.

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