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A simple proof of the Poincaré inequality for a large class of probability measures


 
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1. Title Title of document A simple proof of the Poincaré inequality for a large class of probability measures
 
2. Creator Author's name, affiliation, country Dominique Bakry; LSP, Univ. Toulouse 3
 
2. Creator Author's name, affiliation, country Franck Barthe; LSP, Univ. Toulouse 3
 
2. Creator Author's name, affiliation, country Patrick Cattiaux; LSP, Univ. Toulouse 3
 
2. Creator Author's name, affiliation, country Arnaud Guillin; LATP, Univ. Aix-Marseille 1
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Lyapunov functions, Poincar'e inequality, log-concave measure
 
3. Subject Subject classification 26D10, 47D07, 60G10, 60J60
 
4. Description Abstract Abstract. We give a simple and direct proof of the existence of a spectral gap under some Lyapunov type condition which is satisfied in particular by log-concave probability measures on $\mathbb{R}^n$. The proof is based on arguments introduced in Bakry and al, but for the sake of completeness, all details are provided.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Agence Nationale de la Recherche, Projet IFO
 
7. Date (YYYY-MM-DD) 2008-02-04
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1352
 
10. Identifier Digital Object Identifier 10.1214/ECP.v13-1352
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 13
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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