An almost sure large deviation principle for the Hopfield model

• 成果类型: Article
• 署名作者: Bovier, A; Gayrard, V
• 署名单位: Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1996
• 页码: 1444-1475
• 关键词: Neural networks; gibbs-states; memory; patterns

摘要

We prove a large deviation principle for the finite-dimensional marginals of the Gibbs distribution of the macroscopic ''overlap'' parameters in the Hopfield model in the case where the number of random ''patterns'' M, as a function of the system size N, satisfies lim sup M(N)/N = 0. In this case, the rate function is independent of the disorder for almost all realizations of the patterns.