Exponential inequalities and convergence of moments in the replica-symmetric regime of the Hopfield model
成果类型：
Article
署名作者：
Talagrand, B
署名单位：
Sorbonne Universite; University System of Ohio; Ohio State University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2000
页码：
1393-1469
关键词：
摘要：
In a previous work, we proved the validity of the replica-symmetric solution for the Hopfield model in a nontrivial domain of parameters. This was done at the accuracy of the LLN. In a somewhat larger domain, we obtain a description at the level of the CLT, or, in the terminology of physics, we calculate the fluctuations around the mean field. This is obtained by refining the tools we developed for a rigorous use of the cavity method and proving new a priori estimates about the localization of the Gibbs measure.