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Houdré,
Christian
Houdré,
Christian
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ItemConverse Poincaré Type Inequalities for Convex Functions(Georgia Institute of Technology, 2009-12-07) Bobkov, S. G. ; Houdré, ChristianConverse Poincaré type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution.
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ItemSharp Constants in Some Multiplicative Sobolev Inequalities(Georgia Institute of Technology, 1995-09-16) Bobkov, S. G. ; Houdré, ChristianThe optimal constants in the multiplicative Sobolev inequalities where the gradient is estimated in the L_1-norm and the function in two different Lebesgue norms are found. With the optimal constants, these inequalities turn out to still be equivalent to the isoperimetric property of the balls in the Euclidean space. In the course of the proof, relations between Lorentz and Lebesgue spaces are studied (and also applied to some different measures, e.g., Riesz potentials).
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ItemA Characterization of Gaussian Measures via the Isoperimetric Property of Half-Spaces(Georgia Institute of Technology, 1995-07-25) Bobkov, S. G. ; Houdré, ChristianIf the half-spaces of the form {x\in R^n: x_1 \le c} are extremal in the isoperimetric problem for the product measure \mu^n, n\ge 2, then \mu is Gaussian.
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ItemIsoperimetric Constants for Product Probability Measures(Georgia Institute of Technology, 1995-07-24) Bobkov, S. G. ; Houdré, ChristianA dimension free lower bound is found for isoperimetric constants of product probability measures. From this, some analytic inequalities are derived.
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ItemDimension Free Weak Concentration of Measure Phenomenon(Georgia Institute of Technology, 1995-07-24) Bobkov, S. G. ; Houdré, ChristianFor product probability measures \mu^n, we obtain necessary and sufficient conditions (in terms of \mu) for dimension free isoperimetric inequalities of the form \mu^n (A + h[-1,1]^n)\ge R_h(\mu^n(A)) to hold; for a function R such that R(p) > p, for all (some) p \in (0,1), and for h > 0 large enough. Some questions related to the concentration of measure phenomenon are also discussed.
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ItemVariance of Lipschitz Functions and an Isoperimetric Problem for a Class of Product Measures(Georgia Institute of Technology, 1995-07-10) Bobkov, S. G. ; Houdré, ChristianThe maximal variance of Lipschitz functions (with respect to the \ell_1-distance) of independent random vectors is found. This is then used to solve the isoperimetric problem, uniformly in the class of product probability measures with given variance.