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Rigorous results for the Hopfield model with many patterns
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  • Published: February 1998

Rigorous results for the Hopfield model with many patterns

  • Michel Talagrand1 

Probability Theory and Related Fields volume 110, pages 177–275 (1998)Cite this article

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Summary.

We perform a thorough investigation of the main aspects of the Hopfield model with many patterns. Advances are made toward the validity of the “replica symmetric” solution. Strong evidence of the validity of this solution is given over the entire domain where this validity is conjectured; complete proof is given in a subregion that contains strictly the ergodic region.

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Authors and Affiliations

  1. Equipe d' Analyse, Tour 46, ERA au CNRS No. 754, Université de Paris VI, 4 Place Jussieu, F-75230 Paris Cedex 05, France, , , , , , FR

    Michel Talagrand

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  1. Michel Talagrand
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Received: 22 May 1996 / In revised form: 20 May 1997

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Talagrand, M. Rigorous results for the Hopfield model with many patterns. Probab Theory Relat Fields 110, 177–275 (1998). https://doi.org/10.1007/s004400050148

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  • Issue Date: February 1998

  • DOI: https://doi.org/10.1007/s004400050148

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  • Mathematics Subject Classification (1991): Primary: 82A57. Secondary: 60G15
  • 60E15
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