D
Dominique Bakry
Researcher at Institut de Mathématiques de Toulouse
Publications - 67
Citations - 5056
Dominique Bakry is an academic researcher from Institut de Mathématiques de Toulouse. The author has contributed to research in topics: Sobolev inequality & Heat kernel. The author has an hindex of 25, co-authored 67 publications receiving 4430 citations. Previous affiliations of Dominique Bakry include Paul Sabatier University & Institut Universitaire de France.
Papers
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Book
Analysis and Geometry of Markov Diffusion Operators
TL;DR: Semigroups of bounded operators on a Banach space have been studied in this paper for Riemannian geometry and Markov semigroups have been used for stochastic calculus.
Book ChapterDOI
Logarithmic Sobolev Inequalities
TL;DR: In this article, the logarithmic Sobolev inequalities (LSS inequalities) were studied in infinite dimension and curvature conditions for heat kernel measures, and the fundamental equivalence between the LSS inequalities and smoothing properties of the semigroup in the form of hypercontractivity was shown.
Journal ArticleDOI
Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré
Dominique Bakry,Dominique Bakry,Patrick Cattiaux,Patrick Cattiaux,Arnaud Guillin,Arnaud Guillin +5 more
TL;DR: In this paper, the relationship between two classical approaches for quantitative ergodic properties, Lyapunov type controls and functional inequalities (of Poincare type), is studied. And explicit examples for diffusion processes are studied.
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A simple proof of the Poincaré inequality for a large class of probability measures
TL;DR: In this paper, a simple and direct proof of the existence of a spectral gap under some Lyapunov type condition which is satisfied in particular by log-concave probability measures on ρ √ R n was given.