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Titre
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Poincaré inequalities in probability and geometric analysis
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Description
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The Poincaré, or Poincaré-Wirtinger, inequality controls the variance of a smooth function by its energy as the L^2-norm of its gradient. Put forward by H. Poincaré in 1890 in the study of the spectrum of the Laplace operator on a domain in Euclidean space, it has become a powerful and universal tool in the investigation of spectral lower bounds and convergence to equilibrium in geometric and probabilistic models (manifolds, diffusion operators, graphs, Markov chains etc). We survey in this talk some of the modern illustrations of Poincaré inequalities in probability and analysis, with a particular emphasis on geometric curvature bounds.
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Date
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2012-11-19
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Créateur
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Ledoux, Michel
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Sujet
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Équations aux dérivées partielles
