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Exponential inequalities and convergence of moments in the replica-symmetric regime of the Hopfield model. (English) Zbl 1043.82036

Summary: In a previous work, we proved the validity of the replica-symmetric solution for the Hopfield model in a nontrivial domain of parameters. This was done at the accuracy of the LLN. In a somewhat larger domain, we obtain a description at the level of the 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 “locaiization” of the Gibbs measure.

MSC:

82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
60G99 Stochastic processes
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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