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Michel Ledoux:Poincaré inequalities in probability and geometric analysis
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https://www.youtube.com/watch?v=L_b5D_aEIJc Institut Henri Poincaré Date : 21/11/2012 Lieu : Institut Henri Poincaré Michel Ledoux Homepage:https://perso.math.univ-toulouse.fr/ledoux/ ICM2014 Michel Ledoux——“Heat flows, geometric and functional inequalities” Abstract. Heat flow and semigroup interpolations have developed over the years as a major tool for proving geometric and functional inequalities. Main illustrations presented here range over logarithmic Sobolev inequalities, heat kernel bounds, isoperimetric-type comparison theorems, Brascamp-Lieb inequalities and noise stability. Transportation cost inequalities from optimal mass transport are also part of the picture as consequences of new Harnack-type inequalities. The geometric analysis involves Ricci curvature lower bounds via, as a cornerstone, equivalent gradient bounds on the diffusion semigroups. Most of the results presented here are joint with D. Bakry. Michel Ledoux——“How does the heat equation explore geometric and functional inequalities?” Dominique Bakry , Ivan Gentil , Michel Ledoux——“Analysis and Geometry of Markov Diffusion Operators”:https://doi.org/10.1007/978-3-319-00227-9 Michel Ledoux , Michel Talagrand——“Probability in Banach Spaces——Isoperimetry and Processes”:https://doi.org/10.1007/978-3-642-20212-4 Michel Ledoux——“Concentration of measure and logarithmic Sobolev inequalities”:https://doi.org/10.1007/BFb0096511 Michel Ledoux——“The Concentration of Measure Phenomenon”:https://doi.org/10.1090/surv/089 Michel Ledoux——“Isoperimetry and Gaussian analysis”:https://doi.org/10.1007/BFb0095676 Sergey Bobkov, Michel Ledoux——“One-dimensional empirical measures, order statistics, and Kantorovich transport distances”:https://doi.org/10.1090/memo/1259 Michel Ledoux——“Spectral gap, logarithmic Sobolev constant, and geometric bounds”:https://dx.doi.org/10.4310/SDG.2004.v9.n1.a6 Michel Ledoux——“On Talagrand's deviation inequalities for product measures”:https://doi.org/10.1051/ps:1997103
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