Opinion formation in a heterogeneous population --- a new approach to the Hopfield model

DOI10.1007/s00591-008-0049-zzbMath1193.91123OpenAlexW2135642493MaRDI QIDQ734090

Holger Knöpfel, Matthias Loewe

Publication date: 19 October 2009

Published in: Mathematische Semesterberichte (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00591-008-0049-z

zbMATH Keywords

GrenzwertsätzeHopfield ModellModelle mit diskreten Wahlmöglichkeitenneuronale Netzwerkesoziale Interaktionenungeordnete Systeme

Mathematics Subject Classification ID

Social networks; opinion dynamics (91D30) Neural networks for/in biological studies, artificial life and related topics (92B20) Group preferences (91B10) Models of societies, social and urban evolution (91D10)

Related Items (3)

Multi-group binary choice with social interaction and a random communication structure -- a random graph approach ⋮ Exact recovery in block spin Ising models at the critical line ⋮ Fluctuation results for general block spin Ising models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equilibria in financial markets with heterogeneous agents: a probabilistic perspective
• A central limit theorem for the overlap in the Hopfield model
• An almost sure central limit theorem for the overlap parameters in the Hopfield model
• Lower bounds on the restitution error in the Hopfield model
• Equilibria in systems of social interactions
• Social distance, heterogeneity and social interactions
• A lower bound for the memory capacity in the Potts-Hopfield model
• On the storage capacity of Hopfield models with correlated patterns
• Gibbs states of the Hopfield model in the regime of perfect memory
• Importance sampling for families of distributions
• Moderate deviations for the overlap parameter in the Hopfield model
• Random economies with many interacting agents
• The fluctuations of the overlap in the Hopfield model with finitely many patterns at the critical temperature
• The capacity of \(q\)-state Potts neural networks with parallel retrieval dynamics
• Rigorous results on the thermodynamics of the dilute Hopfield model
• Social Interactions, Local Spillovers and Unemployment
• The capacity of the Hopfield associative memory
• Limit theorems for sums of dependent random variables occurring in statistical mechanics
• Finite Markov Chains and Algorithmic Applications
• Sharp upper bounds on perfect retrieval in the Hopfield model
• Neural networks and physical systems with emergent collective computational abilities.
• Statistical Mechanics of Disordered Systems
• On the Hopfield model at the critical temperature

This page was built for publication: Opinion formation in a heterogeneous population --- a new approach to the Hopfield model