Related papers: On a Correlation Inequality for Cauchy Type Measur…

In the paper we investigate various inequalities for the one-dimensional Cauchy measure. We also consider analogous properties for one-dimensional sections of multidimensional isotropic Cauchy measure. The paper is a continuation of our…

We establish a Cauchy type inequality for the geometric intersection number between two 1-dimensional submanifolds in a surface. Some of the basic results in Thurston's theory of measured laminations on surfaces are derived from the Cauchy…

Using some harmonic extensions on the upper-half plane, and probabilistic representations, and curvature-dimension inequalities with some negative dimensions, we obtain some new opimal functional inequalities of the Beckner type for the…

We review several inequalities concerning Gaussian measures - isoperimetric inequality, Ehrhard's inequality, Bobkov's inequality, S-inequality and correlation conjecture.

We derive an efficient CH-type inequality. Quantum mechanics violates our proposed inequality independent of the detection-efficiency problem.

An inequality is derived for the correlation of two univariate functions operating on symmetric bivariate normal random variables. The inequality is a simple consequence of the Cauchy-Schwarz inequality.

A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.

This note presents families of inequalities for the Gaussian measure of convex sets which extend the recently proven Gaussian correlation inequality in various directions.

In this paper we prove a series of Rogers-Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities, or quasi-concave densities attaining their maximum at the…

We describe some relations between the properties of the Cauchy problem for an ODE and the properties of the Cauchy problem for the associated continuity equation in the class of measures.

The paper is to prove the Gaussian correlation conjecture stating that, under the standard Gaussian measure, the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures.…

A radial probability measure is a probability measure with a density (with respect to the Lebesgue measure) which depends only on the distances to the origin. Consider the Euclidean space enhanced with a radial probability measure. A…

Destructive interference-based photon-phonon antibunching can lead to violations of classical inequalities in optomechanical cavity systems. In this paper, we explore the violation of the classical Cauchy-Schwarz inequality by examining…

We provide a compendium of inequalities between several quantum state distinguishability measures. For each measure these inequalities consist of the sharpest possible upper and lower bounds in terms of another measure. Some of these…

In this paper, we prove the isoperimetric inequality for the anisotropic Gaussian measure and characterize the cases of equality. We also find an example that shows Ehrhard symmetrization fails to decrease for the anisotropic Gaussian…

Motivated by some applications to calculating order of poles of certain (local or global) $L$-functions, the author considers a Cauchy-Schwarz type inequality for representations of SU(2).

In this paper, studying the inverse problem, we establish a curvature compatibility condition on a spherically symmetric Finsler metric. As an application, we characterize the spherically symmetric metrics of scalar curvature. We construct…

Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation…

Based on an apparently new Lagrange-type identity, a Cauchy--Schwarz-type inequality is proved. The mentioned identity is obtained by using certain ``macro'' variables; it is hoped that such a method can be used to prove or produce other…

We study the Riemannian quantiative isoperimetric inequality. We show that direct analogue of the Euclidean quantitative isoperimetric inequality is--in general--false on a closed Riemannian manifold. In spite of this, we show that the…