## Electronic Communications in Probability

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

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 7, 60-66.

Dates
Accepted: 4 February 2008
First available in Project Euclid: 6 June 2016

https://projecteuclid.org/euclid.ecp/1465233434

Digital Object Identifier
doi:10.1214/ECP.v13-1352

Mathematical Reviews number (MathSciNet)
MR2386063

Zentralblatt MATH identifier
1186.26011

Rights

#### Citation

Bakry, Dominique; Barthe, Franck; Cattiaux, Patrick; Guillin, Arnaud. A simple proof of the Poincaré inequality for a large class of probability measures. Electron. Commun. Probab. 13 (2008), paper no. 7, 60--66. doi:10.1214/ECP.v13-1352. https://projecteuclid.org/euclid.ecp/1465233434

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