Electronic Communications in Probability

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

Dominique Bakry, Franck Barthe, Patrick Cattiaux, and Arnaud Guillin

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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

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

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

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Zentralblatt MATH identifier

Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx} 60G10: Stationary processes 60J60: Diffusion processes [See also 58J65]

Lyapunov functions Poincaré inequality log-concave measure

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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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