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Patrick Cattiaux
Researcher at Institut de Mathématiques de Toulouse
Publications - 97
Citations - 3189
Patrick Cattiaux is an academic researcher from Institut de Mathématiques de Toulouse. The author has contributed to research in topics: Ergodic theory & Poincaré inequality. The author has an hindex of 30, co-authored 95 publications receiving 2863 citations. Previous affiliations of Patrick Cattiaux include Paul Sabatier University & Paris West University Nanterre La Défense.
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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.
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Rate of Converrgence for ergodic continuous Markov processes : Lyapunov versus Poincare
TL;DR: In this paper, the relationship between two classical approaches for quantitative ergodic properties, Lyapunov type controls and functional inequalities, was studied, and it was shown that they can be linked through new inequalities.
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Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry
TL;DR: In this paper, the authors introduce the notion of Orlicz hypercontractive semigroups, which describe the integrability improving properties of the Heat semigroup associated to the Boltzmann measures, and derive accurate isoperimetric inequalities for their products.
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Probabilistic approach for granular media equations in the non uniformly convex case
TL;DR: In this paper, a particle system is used to prove both a convergence result with convergence rate and a deviation inequality for solutions of granular media equation when the confinement potential and the interaction potential are no more uniformly convex.