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 and .
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@article{CRMATH_2010__348_3-4_189_0, author = {Panchenko, Dmitry}, title = {The {Ghirlanda{\textendash}Guerra} identities for mixed \protect\emph{p}-spin model}, journal = {Comptes Rendus. Math\'ematique}, pages = {189--192}, publisher = {Elsevier}, volume = {348}, number = {3-4}, year = {2010}, doi = {10.1016/j.crma.2010.02.004}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.02.004/} }
TY - JOUR AU - Panchenko, Dmitry TI - The Ghirlanda–Guerra identities for mixed p-spin model JO - Comptes Rendus. Mathématique PY - 2010 SP - 189 EP - 192 VL - 348 IS - 3-4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.02.004/ DO - 10.1016/j.crma.2010.02.004 LA - en ID - CRMATH_2010__348_3-4_189_0 ER -
%0 Journal Article %A Panchenko, Dmitry %T The Ghirlanda–Guerra identities for mixed p-spin model %J Comptes Rendus. Mathématique %D 2010 %P 189-192 %V 348 %N 3-4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.02.004/ %R 10.1016/j.crma.2010.02.004 %G en %F CRMATH_2010__348_3-4_189_0
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://archive.numdam.org/articles/10.1016/j.crma.2010.02.004/
[1] The Ghirlanda–Guerra identities without averaging, 2009 (preprint) | arXiv
[2] General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity, J. Phys. A, Volume 31 (1998) no. 46, pp. 9149-9155
[3] On differentiability of the Parisi formula, Electron. Comm. Probab., Volume 13 (2008), pp. 241-247
[4] A sequence of approximate solutions to the S-K model for spin glasses, J. Phys. A, Volume 13 (1980), p. L-115
[5] Parisi measures, J. Funct. Anal., Volume 231 (2006) no. 2, pp. 269-286
[6] Parisi formula, Ann. of Math. (2), Volume 163 (2006) no. 1, pp. 221-263
[7] M. Talagrand, Construction of pure states in mean-field models for spin glasses, preprint (2008), Probab. Theory Related Fields, in press, http://www.springerlink.com/content/y507332m08275t67/?p=d35ca639b02943ecae07559b26ef2abf&pi=10
[8] M. Talagrand, Mean field models for spin glasses, manuscript
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