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Author: Houdré, Christian × End date: 1999 × Start date: 1995 × search.filters.applied.f.resourcesubtype: Pre-print ×

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Now showing 1 - 7 of 7
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Sharp Constants in Some Multiplicative Sobolev Inequalities

1995-09-16 , Bobkov, S. G. , Houdré, Christian

The 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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Isoperimetric Constants for Product Probability Measures

1995-07-24 , Bobkov, S. G. , Houdré, Christian

A dimension free lower bound is found for isoperimetric constants of product probability measures. From this, some analytic inequalities are derived.

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Spectral, Criteria, SLLNS and A.S. Convergence of Series of Stationary Variables

1995-04 , Houdré, Christian , Lacey, Michael T.

It is shown here how to extend the spectral characterization of the strong law of large numbers for weakly stationary processes to certain singular averages. For instance, letting {X_t, t \in R^3}, be a weakly stationary field, {X_t} satisfies the usual SLLN (by averaging over balls) if and only if the averages of {X_t} over spheres of increasing radii converge pointwise. The same result in two dimensions is false. This spectral approach also provide a necessary and sufficient condition for the a.s. convergence of some series of stationary variables.

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On the Linear Prediction of Some L^p Random Fields

1995-08 , Cheng, R. , Houdré, Christian

This work is concerned with the prediction problem for a class of L^p-random fields. For this class of fields, we derive prediction error formulas, spectral factorizations, and orthogonal decompositions.

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Dimension Free Weak Concentration of Measure Phenomenon

1995-07-24 , Bobkov, S. G. , Houdré, Christian

For 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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A Characterization of Gaussian Measures via the Isoperimetric Property of Half-Spaces

1995-07-25 , Bobkov, S. G. , Houdré, Christian

If 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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Variance of Lipschitz Functions and an Isoperimetric Problem for a Class of Product Measures

1995-07-10 , Bobkov, S. G. , Houdré, Christian

The 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.

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