Comptes Rendus
no. 11
Probability theory
Probabilities of hitting a convex hull
[Probabilités d'atteinte d'une enveloppe convexe]

Présenté par : the Editorial Board

Zhenxia Liu1 ; Xiangfeng Yang2
1 Blåeldsvägen 12B, Sturefors, Sweden
2 Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 935-940.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.08.015
Zhenxia Liu 1 ; Xiangfeng Yang 2

1 Blåeldsvägen 12B, Sturefors, Sweden
2 Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden 
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Zhenxia Liu; Xiangfeng Yang. Probabilities of hitting a convex hull. Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 935-940. doi : 10.1016/j.crma.2014.08.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.08.015/

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