no. 9-10
Probability Theory/Mathematical Physics
A deletion-invariance property for random measures satisfying the Ghirlanda–Guerra identities
[Une propriété dʼinvariance-suppression des mesures aléatoires vérifiant les identités de Ghirlanda–Guerra]

Présenté par : Michel Talagrand

Panchenko, Dmitry1
1 Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 579-581.

Nous montrons que si une mesure aléatoire discrète sur la boule unité dʼun espace de Hilbert séparable satisfait aux identités de Ghirlanda–Guerra, alors en suprimant aléatoirement la moitié des points et en renormalisant les poids des points restants, on obtient une mesure de même distribution à une rotation près.

We show that if a discrete random measure on the unit ball of a separable Hilbert space satisfies the Ghirlanda–Guerra identities then by randomly deleting half of the points and renormalizing the weights of the remaining points we obtain the same random measure in distribution up to rotations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.04.001
Panchenko, Dmitry 1

1 Department of Mathematics, Texas A&M University, College Station, TX 77843, USA 
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Panchenko, Dmitry. A deletion-invariance property for random measures satisfying the Ghirlanda–Guerra identities. Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 579-581. doi : 10.1016/j.crma.2011.04.001. http://www.numdam.org/articles/10.1016/j.crma.2011.04.001/

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