The Hopfield model with superlinearly many patterns
AbstractWe study the Hopfield model where the ratio α of patterns to sites grows large. We prove that the free energy with inverse temperature β and external field B behaves like βα+γ, where γ=P(2β,B) is the limiting free energy of the Sherrington–Kirkpatrick model with inverse temperature 2β and external field B.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 83 (2013)
Issue (Month): 1 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Gentz, Barbara, 1996. "An almost sure central limit theorem for the overlap parameters in the Hopfield model," Stochastic Processes and their Applications, Elsevier, vol. 62(2), pages 243-262, July.
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