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
Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields
Download PDF
Download PDF
  • Published: August 2001

Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields

  • Filippo Cesi1 

Probability Theory and Related Fields volume 120, pages 569–584 (2001)Cite this article

  • 468 Accesses

  • 49 Citations

  • Metrics details

Abstract.

We show that the entropy functional exhibits a quasi-factorization property with respect to a pair of weakly dependent σ-algebras. As an application we give a simple proof that the Dobrushin and Shlosmans complete analyticity condition, for a Gibbs specification with finite range summable interaction, implies uniform logarithmic Sobolev inequalities. This result has been previously proven using several different techniques. The advantage of our approach is that it relies almost entirely on a general property of the entropy, while very little is assumed on the Dirichlet form. No topology is introduced on the single spin space, thus discrete and continuous spins can be treated in the same way.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Università di Roma “La Sapienza”, P. le A. Moro 2, 00185 Roma, Italy and INFM Unità di Roma “La Sapienza”. e-mail: filippo.cesi@roma1.infn.it, , , , , , IT

    Filippo Cesi

Authors
  1. Filippo Cesi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 7 July 2000 / Revised version: 10 October 2000 / Published online: 5 June 2001

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Cesi, F. Quasi-factorization of the entropy and logarithmic Sobolev inequalities for Gibbs random fields. Probab Theory Relat Fields 120, 569–584 (2001). https://doi.org/10.1007/PL00008792

Download citation

  • Issue Date: August 2001

  • DOI: https://doi.org/10.1007/PL00008792

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

  • Mathematics Subject Classification (2000): 82B20, 82C20, 39B62
  • Key words or phrases: Entropy – Logarithmic Sobolev inequalities – Gibbs measures
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