WIAS Preprint No. 95, (1994)

Large deviation principles for the Hopfield model and the Kac-Hopfield model


  • Bovier, Anton
  • Gayrard, Véronique
  • Picco, Pierre

2010 Mathematics Subject Classification

  • 60K35 82B44 82C32




We study the Kac version of the Hopfield model and prove a Lebowitz-Penrose theorem for the distributions of the overlap parameters. At the same time, we prove a large deviation principle for the standard Hopfield model with infinitely many patterns.

Appeared in

  • Probab. Theory Related Fields, 101 (1995), pp. 511--546

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