Functional inequalities for heavy tailed distributions and application to isoperimetry.
Cattiaux, Patrick, Gozlan, Nathael, Guillin, Arnaud, Roberto, Cyril (2010)
Electronic Journal of Probability [electronic only]
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Cattiaux, Patrick, Gozlan, Nathael, Guillin, Arnaud, Roberto, Cyril (2010)
Electronic Journal of Probability [electronic only]
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Michel Ledoux (2011)
Journées Équations aux dérivées partielles
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We survey analytic and geometric proofs of classical logarithmic Sobolev inequalities for Gaussian and more general strictly log-concave probability measures. Developments of the last decade link the two approaches through heat kernel and Hamilton-Jacobi equations, inequalities in convex geometry and mass transportation.
Yohann de Castro (2011)
Annales mathématiques Blaise Pascal
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In a recent paper A. Cianchi, N. Fusco, F. Maggi, and A. Pratelli have shown that, in the Gauss space, a set of given measure and almost minimal Gauss boundary measure is necessarily close to be a half-space. Using only geometric tools, we extend their result to all symmetric log-concave measures on the real line. We give sharp quantitative isoperimetric inequalities and prove that among sets of given measure and given asymmetry (distance to half line, i.e. distance to sets...
Song, Renming (2006)
Electronic Journal of Probability [electronic only]
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Romesh Kumar, Kanwar Jatinder Singh (2006)
Extracta Mathematicae
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In this paper, we characterize boundedness and compactness of weighted composition operators on the Dirichlet space and obtain the estimates for the essential norm.
Jan Malczak (1992)
Annales Polonici Mathematici
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We define the Foiaş solutions of the transport equation and we prove that the strong asymptotic stability of the Foiaş solutions is equivalent to the asymptotic stability of the solutions of the transport equation in L¹.
Pinelis, Iosif (2006)
Electronic Journal of Probability [electronic only]
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Nicola Gigli (2014)
Analysis and Geometry in Metric Spaces
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Frédéric Hérau (2002)
Journées équations aux dérivées partielles
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We consider the Fokker-Planck equation with a confining or anti-confining potential which behaves at infinity like a possibly high degree homogeneous function. Hypoellipticity techniques provide the well-posedness of the weak-Cauchy problem in both cases as well as instantaneous smoothing and exponential trend to equilibrium. Lower and upper bounds for the rate of convergence to equilibrium are obtained in terms of the lowest positive eigenvalue of the corresponding Witten laplacian,...