Logarithmic Sobolev inequalities for unbounded spin systems revisited
Michel Ledoux (2001)
Séminaire de probabilités de Strasbourg
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Michel Ledoux (2001)
Séminaire de probabilités de Strasbourg
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Michel Ledoux (1999)
Séminaire de probabilités de Strasbourg
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Radosław Adamczak (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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Radosław Adamczak, Michał Strzelecki (2015)
Studia Mathematica
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We provide a mild sufficient condition for a probability measure on the real line to satisfy a modified log-Sobolev inequality for convex functions, interpolating between the classical log-Sobolev inequality and a Bobkov-Ledoux type inequality. As a consequence we obtain dimension-free two-level concentration results for convex functions of independent random variables with sufficiently regular tail decay. We also provide a link between modified log-Sobolev...
Petteri Harjulehto, Peter Hästö, Mika Koskenoja, Susanna Varonen (2005)
Banach Center Publications
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In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.
Andrea Cianchi, Nicola Fusco, F. Maggi, A. Pratelli (2009)
Journal of the European Mathematical Society
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Andrea Cianchi, Luboš Pick, Lenka Slavíková (2014)
Banach Center Publications
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We survey results from the paper [CPS] in which we developed a new sharp iteration method and applied it to show that the optimal Sobolev embeddings of any order can be derived from isoperimetric inequalities. We prove thereby that the well-known link between first-order Sobolev embeddings and isoperimetric inequalities translates to embeddings of any order, a fact that had not been known before. We show a general reduction principle that reduces Sobolev type inequalities of any order...
Kutateladze, S.S. (2001)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Djalil Chafaï (2002)
Séminaire de probabilités de Strasbourg
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Ershov, Yu.L., Kutateladze, S.S. (2009)
Sibirskij Matematicheskij Zhurnal
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V. M. Tikhomirov (1989)
Banach Center Publications
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A. Pełczyński, K. Senator (1986)
Studia Mathematica
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Matteo Bonforte, Gabriele Grillo (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.
Djalil Chafaï, Florent Malrieu (2010)
Annales de l'I.H.P. Probabilités et statistiques
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Mixtures are convex combinations of laws. Despite this simple definition, a mixture can be far more subtle than its mixed components. For instance, mixing gaussian laws may produce a potential with multiple deep wells. We study in the present work fine properties of mixtures with respect to concentration of measure and Sobolev type functional inequalities. We provide sharp Laplace bounds for Lipschitz functions in the case of generic mixtures, involving a transportation cost diameter...