Results 1  10
of
17
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
, 2004
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Characterization of Talagrand’s like transportationcost inequalities on the real line
, 2006
"... In this paper, we give necessary and sufficient conditions for Talagrand’s like transportation cost inequalities on the real line. This brings a new wide class of examples of probability measures enjoying a dimensionfree concentration of measure property. Another byproduct is the characterization ..."
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Cited by 14 (4 self)
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In this paper, we give necessary and sufficient conditions for Talagrand’s like transportation cost inequalities on the real line. This brings a new wide class of examples of probability measures enjoying a dimensionfree concentration of measure property. Another byproduct is the characterization of modified LogSobolev inequalities for Logconcave probability measures on R.
TRANSPORT INEQUALITIES. A SURVEY
"... Abstract. This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch their links with other functional inequalities and also large deviation theory. ..."
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Cited by 7 (1 self)
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Abstract. This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch their links with other functional inequalities and also large deviation theory.
Weak logarithmic Sobolev inequalities and entropic convergence
, 2005
"... In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner inequalities...). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion ..."
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Cited by 3 (2 self)
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In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner inequalities...). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion semigroup. In particular, we exhibit an example where Poincaré inequality can not be used for deriving entropic convergence whence weak logarithmic Sobolev inequality ensures the result.
A new characterization of Talagrand’s transportentropy inequalities and applications
, 2011
"... We give a characterization of transportentropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley–Stroock perturbation lemma). ..."
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Cited by 3 (3 self)
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We give a characterization of transportentropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley–Stroock perturbation lemma).
HamiltonJacobi equations on metric spaces and transport entropy inequalities
, 2012
"... Abstract. We prove an HopfLaxOleinik formula for the solutions of some HamiltonJacobi equations on a general metric space. As a first consequence, we show in full generality that the logSobolev inequality is equivalent to an hypercontractivity property of the HamiltonJacobi semigroup. Asasecon ..."
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Cited by 3 (1 self)
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Abstract. We prove an HopfLaxOleinik formula for the solutions of some HamiltonJacobi equations on a general metric space. As a first consequence, we show in full generality that the logSobolev inequality is equivalent to an hypercontractivity property of the HamiltonJacobi semigroup. Asasecondconsequence, weprovethatTalagrand’s transportentropy inequalities in metric space are characterized in terms of logSobolev inequalities restricted to the class of cconvex functions. hal00795829, version 1 1 Mar 2013 1.
Poincaré inequalities for non euclidean metrics and . . .
, 2007
"... In this paper, we consider Poincaré inequalities for non euclidean metrics on R d. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for a large scope of concentration rate: between exponential and gaussian ..."
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Cited by 2 (0 self)
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In this paper, we consider Poincaré inequalities for non euclidean metrics on R d. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for a large scope of concentration rate: between exponential and gaussian and beyond. We give different equivalent functional forms of these Poincaré type inequalities in terms of transportationcost inequalities and infimum convolution inequalities. Workable sufficient conditions are given and a comparison is made with generalized BecknerLatalaOleszkiewicz inequalities.
From the PrékopaLeindler inequality to modified logarithmic Sobolev
, 710
"... We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the PrékopaLeindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on R n, with a strictly convex and superlinear potential. This inequality implies modi ..."
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Cited by 2 (0 self)
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We develop in this paper an improvement of the method given by S. Bobkov and M. Ledoux in [BL00]. Using the PrékopaLeindler inequality, we prove a modified logarithmic Sobolev inequality adapted for all measures on R n, with a strictly convex and superlinear potential. This inequality implies modified logarithmic Sobolev inequality, developed in [GGM05, GGM07], for all uniformly strictly convex potential as well as the Euclidean logarithmic Sobolev inequality. Résumé Dans cet article nous amélirons la méthode exposée par S. Bobkov et M. Ledoux dans [BL00]. En utilisant l’inégalité de PrékopaLeindler, nous prouvons une inégalité de Sobolev logarithmique modifiée, adaptée à toutes les mesures sur R n possédant un potentiel strictement convexe et superlinéaire. Cette inégalité implique en particulier une inégalité de Sobolev logarithmique modifiée, développée dans [GGM05, GGM07], pour les mesures ayant un potentiel uniformément strictement convexe mais aussi une inégalité de Sobolev logarithmique de type euclidien. 1
Convex Sobolev inequalities and spectral gap
, 2005
"... This note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by ..."
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This note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux [11] and Carlen and Loss [10] for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities with constants which are uniformly bounded in the limit approaching the logarithmic Sobolev inequalities. We recover the case of the logarithmic Sobolev inequalities as a special case.
PrékopaLeindler inequality
, 2008
"... Logarithmic Sobolev inequality for logconcave measure from ..."