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Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
, 2004
"... ..."
Hypercontractivity for perturbed diffusion semigroups
 ANN. FAC. DES SC. DE TOULOUSE
, 2005
"... µ being a nonnegative measure satisfying some LogSobolev inequality, we give conditions on F for the Boltzmann measure ν = e −2F µ to also satisfy some LogSobolev inequality. This paper improves and completes the final section in [6]. A general sufficient condition and a general necessary conditio ..."
Abstract

Cited by 20 (14 self)
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µ being a nonnegative measure satisfying some LogSobolev inequality, we give conditions on F for the Boltzmann measure ν = e −2F µ to also satisfy some LogSobolev inequality. This paper improves and completes the final section in [6]. A general sufficient condition and a general necessary condition are given and examples are explicitly studied.
AND
, 2003
"... Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. In particular if a logarithmic Sobolev inequality implies T2, we are able to give examples for which T2 holds but the logarithm ..."
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Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. In particular if a logarithmic Sobolev inequality implies T2, we are able to give examples for which T2 holds but the logarithmic Sobolev inequality does not hold. This answers to a question left open by Otto and Villani [21] and Bobkov, Gentil and Ledoux [4], and furnishes (in a Riemannian setting) the analogue of the well known criterion by Bobkov and Götze for the linear transportation cost inequality T1 [5] (also see [12]). The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in the spirit of the modified logarithmicSobolev inequalities by Bobkov and Ledoux [6], that are shown to hold as soon as a Poincaré inequality is satisfied.
AND
, 2003
"... Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. In particular if a logarithmic Sobolev inequality implies T2, we are able to give examples for which T2 holds but the logarithm ..."
Abstract
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Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. In particular if a logarithmic Sobolev inequality implies T2, we are able to give examples for which T2 holds but the logarithmic Sobolev inequality does not hold. This answers to a question left open by Otto and Villani [20] and Bobkov, Gentil and Ledoux [3], and furnishes (in a Riemannian setting) the analogue of the well known criterion by Bobkov and Götze for the linear transportation cost inequality T1 [4] (also see [11]). The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in the spirit of the modified logarithmicSobolev inequalities by Bobkov and Ledoux [5], that are shown to hold as soon as a Poincaré inequality is satisfied.
AND
, 2003
"... Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in ..."
Abstract
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Abstract. We show that the quadratic transportation cost inequality T2 is equivalent to both a Poincaré inequality and a strong form of the Gaussian concentration property. The main ingredient in the proof is a new family of inequalities, called modified quadratic transportation cost inequalities in the spirit of the modified logarithmicSobolev inequalities by Bobkov and Ledoux [6], that are shown to hold as soon as a Poincaré inequality is satisfied.
Set Mn = 1
, 2005
"... Abstract. The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning principle for thin sets). Applications to stochastic mechanics or calibration problems for diff ..."
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Abstract. The aim of this paper is to use non asymptotic bounds for the probability of rare events in the Sanov theorem, in order to study the asymptotics in conditional limit theorems (Gibbs conditioning principle for thin sets). Applications to stochastic mechanics or calibration problems for diffusion processes are discussed. 1.