Comptes Rendus
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

Dmitry Panchenko1
1 Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
Comptes Rendus. Mathématique, Volume 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
Dmitry Panchenko 1

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

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[4] D. Panchenko A connection between Ghirlanda–Guerra identities and ultrametricity, Ann. Probab., Volume 38 (2010) no. 1, pp. 327-347

[5] D. Panchenko On the Dovbysh–Sudakov representation result, Electron. Commun. Probab., Volume 15 (2010), pp. 330-338

[6] M. Talagrand Construction of pure states in mean-field models for spin glasses, Probab. Theory Related Fields, Volume 148 (2010) no. 3–4, pp. 601-643

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[8] M. Talagrand, Mean-Field Models for Spin Glasses, second edition of [7], in press. First volume was published: http://www.springer.com/mathematics/probability/book/978-3-642-15201-6. Vol. 2 will appear in Ergebnisse Series, vol. 55.

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