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Topics in Optimal Transportation
Introduction The Kantorovich duality Geometry of optimal transportation Brenier's polar factorization theorem The Monge-Ampere equation Displacement interpolation and displacement convexity GeometricExpand
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Optimal Transport: Old and New
Couplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- CyclicalExpand
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Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
Abstract We show that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6 , 587–600) for the Gaussian measure, are implied by logarithmic SobolevExpand
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Ricci curvature for metric-measure spaces via optimal transport
We dene a notion of a measured length space X having nonnegative N-Ricci curvature, for N 2 [1;1), or having1-Ricci curvature bounded below byK, forK2 R. The denitions are in terms of theExpand
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Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory
This text has appeared with minor modifications in the Handbook of Mathematical Fluid Dynamics (Vol. 1), edited by S. Friedlander and D. Serre, published by Elsevier Science (2002). I have performedExpand
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On a New Class of Weak Solutions to the Spatially Homogeneous Boltzmann and Landau Equations
This paper deals with the spatially homogeneous Boltzmann equation when grazing collisions are involved.We study in a unified setting the Boltzmann equation without cut-off, the Fokker-Planck-LandauExpand
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Entropy Dissipation and Long-Range Interactions
Abstract:We study Boltzmann's collision operator for long-range interactions, i.e., without Grad's angular cut-off assumption. We establish a functional inequality showing that the entropyExpand
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Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4]Expand
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On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation
As part of our study of convergence to equilibrium for spatially inhomogeneous kinetic equations, started in [21], we derive estimates on the rate of convergence to equilibrium for solutions of theExpand
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Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces
We establish quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particleExpand
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