Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
On the Hopfield model at the critical temperature
Download PDF
Download PDF
  • Published: October 2001

On the Hopfield model at the critical temperature

  • Michel Talagrand1 

Probability Theory and Related Fields volume 121, pages 237–268 (2001)Cite this article

  • 78 Accesses

  • 4 Citations

  • Metrics details

Abstract.

We study the Hopfield model at temperature 1, when thenumber M(N) of patterns grows a bit slower than N. We reach a goodunderstanding of the model whenever M(N)≤N/(log N)11. For example, we show that if M(N)→∞, for two typical configurations σ 1, σ 2, (∑ i ≤ N σ1 i σ2 i )2 is close to NM(N).

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Equipe d'Analyse, Tour 46, ESA au CNRS no. 7064, Université de Paris VI, 4, Place Jussieu, 75230 Paris Cedex 05, France (e-mail: mit@ccr.jussieu.fr), , , , , , FR

    Michel Talagrand

Authors
  1. Michel Talagrand
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 15 December 1999 / Revised version: 8 December 2000 / Published online: 23 August 2001

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Talagrand, M. On the Hopfield model at the critical temperature. Probab Theory Relat Fields 121, 237–268 (2001). https://doi.org/10.1007/PL00008804

Download citation

  • Issue Date: October 2001

  • DOI: https://doi.org/10.1007/PL00008804

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Critical Temperature
  • Typical Configuration
  • Hopfield Model
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature