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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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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DOI: https://doi.org/10.1007/s004400050148
- Mathematics Subject Classification (1991): Primary: 82A57. Secondary: 60G15
- 60E15