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Probability Theory and Related Fields

, Volume 110, Issue 2, pp 177–275 | Cite as

Rigorous results for the Hopfield model with many patterns

  • Michel Talagrand
Article

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.

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

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

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