Self-averaging in a Class of Generalized Hopfield Models#
نویسنده
چکیده
We prove the almost sure convergence to zero of the uctuations of the free energy, resp. local free energies, in a class of disordered mean-eld spin systems that generalize the Hoppeld model in two ways: 1) Multi-spin interactions are permitted and 2) the random variables i describing thèpatterns' can have arbitrary distributions with mean zero and nite 4+-th moments. The number of patterns, M, is allowed to be an arbitrary multiple of the systemsize. This generalizes a previous result of Bovier, Gayrard, and Picco BGP3] for the standard Hoppeld model, and improves a result of Feng and Tirozzi FT] that required M to be a nite constant. Note that the convergence of the mean of the free energy is not proven.
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