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Exponential Integrability and Transportation Cost Related to Logarithmic Sobolev Inequalities

Abstract We study some problems on exponential integrability, concentration of measure, and transportation cost related to logarithmic Sobolev inequalities. On the real line, we then give a… Expand

Isoperimetric and Analytic Inequalities for Log-Concave Probability Measures

- S. Bobkov
- Mathematics
- 1999

We discuss an approach, based on the Brunn–Minkowski inequality, to isoperimetric and analytic inequalities for probability measures on Euclidean space with logarithmically concave densities. In… Expand

Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution

Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every… Expand

From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities

Abstract. We develop several applications of the Brunn—Minkowski inequality in the Prékopa—Leindler form. In particular, we show that an argument of B. Maurey may be adapted to deduce from the… Expand

One-dimensional empirical measures, order
statistics, and Kantorovich transport
distances

This work is devoted to the study of rates of convergence of the empirical measures μn = 1 n ∑n k=1 δXk , n ≥ 1, over a sample (Xk)k≥1 of independent identically distributed real-valued random… Expand

On Modified Logarithmic Sobolev Inequalities for Bernoulli and Poisson Measures

We show that for any positive functionfon the discrete cube {0, 1}n,Entμnp(f)⩽pqEμnp1f|Df|2whereμnpis the product measure of the Bernoulli measure with probability of successp, as well as related… Expand

Extremal properties of half-spaces for log-concave distributions

- S. Bobkov
- Mathematics
- 1996

n w x n where m s m = ??? = m is the product measure in R , D s y1, 1 is the n n-dimensional cube in R n and the infimum is then over all Borel-measurable n n . sets A ; R of measure m A G p; 0 - p -… Expand

Isoperimetric constants for product probability measures

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

Weighted poincaré-type inequalities for cauchy and other convex measures

Brascamp-Lieb-type, weighted Poincare-type and related analytic inequalities are studied for multidimensional Cauchy distributions and more general κ-concave probability measures (in the hierarchy of… Expand

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