Displaying similar documents to “On Talagrand's deviation inequalities for product measures”

Sobolev inequalities for probability measures on the real line

F. Barthe, C. Roberto (2003)

Studia Mathematica

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We give a characterization of those probability measures on the real line which satisfy certain Sobolev inequalities. Our starting point is a simpler approach to the Bobkov-Götze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latała-Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures...

Poincaré inequalities and hitting times

Patrick Cattiaux, Arnaud Guillin, Pierre André Zitt (2013)

Annales de l'I.H.P. Probabilités et statistiques

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Equivalence of the spectral gap, exponential integrability of hitting times and Lyapunov conditions is well known. We give here the correspondence (with quantitative results) for reversible diffusion processes. As a consequence, we generalize results of Bobkov in the one dimensional case on the value of the Poincaré constant for log-concave measures to superlinear potentials. Finally, we study various functional inequalities under different hitting times integrability conditions (polynomial,…)....