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

   
@article{ECP1352,
	author = {Dominique Bakry and Franck Barthe and Patrick Cattiaux and Arnaud Guillin},
	title = {A simple proof of the Poincaré inequality for a large class of probability measures},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {Lyapunov functions, Poincar'e inequality, log-concave measure},
	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.},
	pages = {no. 7, 60-66},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1352},    
        url = {http://ecp.ejpecp.org/article/view/1352}}