Restricted Prékopa–Leindler inequality

Restricted Prékopa-leindler Inequality

We prove a functional version of the Brunn-Minkowski inequality for restricted sums obtained by Szarek and Voicu-lescu. We only consider Lebesgue-measurable subsets of R n , and for A ⊂ R n , we denote its volume by |A|. If A, B ⊂ R n , their Minkowski sum is defined by A + B = {x + y, (x, y) ∈ A × B}. The classical Brunn-Minkowski inequality provides a lower bound for its volume. In their stud...

Volumes of Restricted Minkowski Sums and the Free Analogue of the Entropy Power Inequality

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability (for an introduction see [9]). The analogue of entropy in the free context was introduced by the second named author in [8]. Here we show that Shannon's entropy power inequality ([6],[1]) has an analogue for the free entropy χ(X...

Admissible Estimators in the General Multivariate Linear Model with Respect to Inequality Restricted Parameter Set

By using themethods of linear algebra andmatrix inequality theory, we obtain the characterization of admissible estimators in the general multivariate linear model with respect to inequality restricted parameter set. In the classes of homogeneous and general linear estimators, the necessary and suffcient conditions that the estimators of regression coeffcient function are admissible are establi...

Education , Inequality and Income Inequality

In this paper we propose to measure inequality of educational achievements by constructing a Gini index on educational attainments. We then use the proposed measure to analyse the relationship between inequality in incomes and educational achievements (in terms of both the average attainments and its concentration). Even if theoretical considerations suggest a non-linear relationship between th...

Corruption And Inequality