Universality of Ghirlanda-Guerra identities and spin distributions in mixed $p$-spin models
Autor: | Chen, Yu-Ting |
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Rok vydání: | 2016 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | We prove universality of the Ghirlanda-Guerra identities and spin distributions in the mixed $p$-spin models. The assumption for the universality of the identities requires exactly that the coupling constants have zero means and finite variances, and the result applies to the Sherrington-Kirkpatrick model. As an application, we obtain weakly convergent universality of spin distributions in the generic $p$-spin models under the condition of two matching moments. In particular, certain identities for 3-overlaps and 4-overlaps under the Gaussian disorder follow. Under the stronger mode of total variation convergence, we find that universality of spin distributions in the mixed $p$-spin models holds if mild dilution of connectivity by the Viana-Bray diluted spin glass Hamiltonians is present and the first three moments of coupling constants in the mixed $p$-spin Hamiltonians match. These universality results are in stark contrast to the characterization of spin distributions in the undiluted mixed $p$-spin models, which is known up to now that four matching moments are required in general. Comment: 26 pages.To appear in Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques |
Databáze: | arXiv |
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