The Annals of Probability

An almost sure large deviation principle for the Hopfield model

Anton Bovier and Véronique Gayrard

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Probab., Volume 24, Number 3 (1996), 1444-1475.

Dates
First available in Project Euclid: 9 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1065725188

Digital Object Identifier
doi:10.1214/aop/1065725188

Mathematical Reviews number (MathSciNet)
MR1411501

Zentralblatt MATH identifier
0871.60022

Subjects
Primary: 60F10: Large deviations 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.) 82C32: Neural nets [See also 68T05, 91E40, 92B20]

Keywords
Hopfield model neural networks self-averaging large deviations

Citation

Bovier, Anton; Gayrard, Véronique. An almost sure large deviation principle for the Hopfield model. Ann. Probab. 24 (1996), no. 3, 1444--1475. doi:10.1214/aop/1065725188. https://projecteuclid.org/euclid.aop/1065725188


Export citation