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
Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution
Download PDF
Download PDF
  • Published: March 1997

Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution

  • S. Bobkov1 &
  • M. Ledoux2 

Probability Theory and Related Fields volume 107, pages 383–400 (1997)Cite this article

  • 533 Accesses

  • 87 Citations

  • Metrics details

Summary.

We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper bounds on spectral gaps.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Department of Mathematics, Syktyvkar University, 167001 Syktyvkar, Russia , , , , , , RU

    S. Bobkov

  2. Département de Mathématiques, Laboratoire de Statistique et Probabilités associé au CNRS, Université Paul-Sabatier, F-31062 Toulouse, France, , , , , , FR

    M. Ledoux

Authors
  1. S. Bobkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Ledoux
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 10 June 1996 / In revised form: 9 August 1996

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bobkov, S., Ledoux, M. Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution. Probab Theory Relat Fields 107, 383–400 (1997). https://doi.org/10.1007/s004400050090

Download citation

  • Issue Date: March 1997

  • DOI: https://doi.org/10.1007/s004400050090

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: Primary: 60E15
  • 28A35
  • 60E99; Secondary: 58C40
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