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

DOI10.1007/BF01202783zbMath0826.60090MaRDI QIDQ1804992

Véronique Gayrard, Anton Bovier, Pierre Picco

Publication date: 14 November 1995

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

zbMATH Keywords

large deviation principleHopfield modelstatistical mechanicsoverlap parameterGärtner-Ellis theorems

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) Large deviations (60F10) Neural nets applied to problems in time-dependent statistical mechanics (82C32)

Related Items (6)

On the norm and eigenvalue distribution of large random matrices ⋮ The low-temperature phase of Kac-Ising models ⋮ On the free energy of the Hopfield model ⋮ Unnamed Item ⋮ On the storage capacity of Hopfield models with correlated patterns ⋮ Gibbs states of the Hopfield model with extensively many patterns.

Cites Work

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• Gibbs states of the Hopfield model in the regime of perfect memory
• Rigorous bounds on the storage capacity of the dilute Hopfield model
• Thermodynamic limit of the \(q\)-state Potts-Hopfield model with infinitely many patterns
• The replica-symmetric solution without replica trick for the Hopfield model
• The free energy of a class of Hopfield models
• On Large Deviations from the Invariant Measure
• A free energy bound for the Hopfield model
• On the van der Waals Theory of the Vapor-Liquid Equilibrium. I. Discussion of a One-Dimensional Model
• Rigorous Treatment of the Van Der Waals-Maxwell Theory of the Liquid-Vapor Transition
• Neural networks and physical systems with emergent collective computational abilities.
• BEHAVIOR IN LARGE DIMENSIONS OF THE POTTS AND HEISENBERG MODELS

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