Exponential inequalities and convergence of moments in the replica-symmetric regime of the Hopfield model
Talagrand, Michel
Ann. Probab., Tome 28 (2000) no. 1, p. 1393-1469 / Harvested from Project Euclid
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In a previous work,we proved the validity ofthe replica-symmetric solution for the Hop field model in a nontrivial domain of parameters. This was done at the accuracy ofthe LLN In a somewhat larger domain, we obtain a description at the level ofthe CLT, or, in the terminology of physics, we calculate the fluctuations around the mean field. This is obtained by refining the tools we developed for a rigorous use of the cavity method and proving new a priori estimates about the “localization”of the Gibbs measure.
Publié le : 2000-10-14
Classification:  Spin glass,  Hopfield model,  replica-symmetric solution,  82D30,  60G99 
@article{1019160495,
     author = {Talagrand, Michel},
     title = {Exponential inequalities and convergence of moments in the
		 replica-symmetric regime of the Hopfield model},
     journal = {Ann. Probab.},
     volume = {28},
     number = {1},
     year = {2000},
     pages = { 1393-1469},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1019160495}
}

Talagrand, Michel. Exponential inequalities and convergence of moments in the
		 replica-symmetric regime of the Hopfield model. Ann. Probab., Tome 28 (2000) no. 1, pp.  1393-1469. http://gdmltest.u-ga.fr/item/1019160495/