The fluctuations of the overlap in the Hopfield model with finitely many patterns at the critical temperature
type: Item
instance of: scholarly article
title: The fluctuations of the overlap in the Hopfield model with finitely many patterns at the critical temperature
zbMATH Open document ID: 0953.60094
author: Barbara Gentz
author: M. Löwe
publication date: 2001-01-22T00:00:00Z
review text: The authors consider the Hopfield model with a finite number of patterns at the critical temperature \(\beta=1\). It is known that the so-called overlap parameter, \(m_N\), converges to zero under the Gibbs measure almost surely when the system size, \(N\), tends to infinity. The authors prove a non-standard limit theorem for the blown up overlap, \(N^{1/4} m_N\), in the sense that this quantity converges in law to some random variable whose probability density is random with respect to the quenched disorder and explicitly given in terms of a function of some family of Gaussian random variables.
reviewed by: Anton Bovier
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B44
zbMATH DE Number: 1389148
zbMATH Keywords: opfiled model
zbMATH Keywords: disordered spin systems
zbMATH Keywords: central limit theorem
zbMATH Keywords: critical point
MaRDI profile type: Publication
full work available at URL: s004400050241
OpenAlex ID: W1966135684
DOI: 10.1007/S004400050241
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1389148