Summary
We study the Kac version of the Hopfield model and prove a Lebowitz-Penrose theorem for the distribution of the overlap parameters. At the same time, we prove a large deviation principle for the standard Hopfield model with infinitely many patterns.
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Work partially supported by the Commission of the European Communities under contract No. SC1-CT91-0695
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Bovier, A., Gayrard, V. & Picco, P. Large deviation principles for the Hopfield model and the Kac-Hopfield model. Probab. Th. Rel. Fields 101, 511–546 (1995). https://doi.org/10.1007/BF01202783
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DOI: https://doi.org/10.1007/BF01202783