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

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.

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).

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

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