no. 3-4
Probability Theory/Mathematical Physics
The Ghirlanda–Guerra identities for mixed p-spin model
[Les identités de Ghirlanda–Guerra pour les mélanges de modèles à p-spin]

Présenté par : Michel Talagrand

Panchenko, Dmitry1
1 Department of Mathematics, Texas A&M University, 77843 College Station, TX, USA
Comptes Rendus. Mathématique, Tome 348 (2010) no. 3-4, pp. 189-192.

Nous montrons que sous les conditions connues pour impliquer la validité de la formule de Parisi, si l'Hamiltonien du modè le générique de Sherrington–Kirkpatrick Hamiltonien contient un « Hamiltonien de p-spin » alors les identités de Ghirlanda–Guerra pour la puissance p des recouvrements sont valides dans un sens fort (et pas seulement en moyenne sur les parametres).

We show that, under the conditions known to imply the validity of the Parisi formula, if the generic Sherrington–Kirkpatrick Hamiltonian contains a p-spin term then the Ghirlanda–Guerra identities for the pth power of the overlap hold in a strong sense without averaging. This implies strong version of the extended Ghirlanda–Guerra identities for mixed p-spin models than contain terms for all even p⩾2 and p=1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.02.004
Panchenko, Dmitry 1

1 Department of Mathematics, Texas A&M University, 77843 College Station, TX, USA 
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Panchenko, Dmitry. The Ghirlanda–Guerra identities for mixed p-spin model. Comptes Rendus. Mathématique, Tome 348 (2010) no. 3-4, pp. 189-192. doi : 10.1016/j.crma.2010.02.004. http://www.numdam.org/articles/10.1016/j.crma.2010.02.004/

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