Gibbs states of the Hopfield model in the regime of perfect memory

DOI10.1007/BF01193704zbMath0810.60094MaRDI QIDQ1343607

Véronique Gayrard, Pierre Picco, Anton Bovier

Publication date: 4 April 1995

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

Bernoulli measuresconvergent sequences of measuresinfinite number of infinite volume Gibbs measuresthermodynamic properties of the Hopfield model

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Neural nets applied to problems in time-dependent statistical mechanics (82C32)

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Cites Work

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• The eigenvalues of random symmetric matrices
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• Thermodynamic limit of the \(q\)-state Potts-Hopfield model with infinitely many patterns
• The replica-symmetric solution without replica trick for the Hopfield model
• Rigorous results on the thermodynamics of the dilute Hopfield model
• The free energy of a class of Hopfield models
• A Remark on Stirling's Formula
• Modeling Brain Function
• A free energy bound for the Hopfield model
• Neural networks and physical systems with emergent collective computational abilities.

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