相关论文: Volume Inequalities for Isotropic Measures

Presenting simple coarse-grained models of isotropic solids and fluids in $d=1$, $2$ and $3$ dimensions we investigate the correlations of the instantaneous pressure and its ideal and excess contributions at either imposed pressure…

We show that a strong version of the Brascamp--Lieb inequality for symmetric log-concave measure with $\alpha$-homogeneous potential $V$ is equivalent to a $p$-Brunn--Minkowski inequality for level sets of $V$ with some $p(\alpha,n)<0$. We…

We derive two concentration inequalities for linear functions of log-concave distributions: an enhanced version of the classical Brascamp--Lieb concentration inequality, and an inequality quantifying log-concavity of marginals in a manner…

The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr.~on the reverse question: Every convex body has a linear image whose…

Finding all Bell inequalities for a given number of parties, measurement settings, and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can…

We derive a Bell-type inequality for observables with arbitrary spectra. For the case of continuous variable systems we propose a possible experimental violation of this inequality, by using squeezed light and homodyne detection together…

Our main contribution is a concentration inequality for the symmetric volume difference of a $ C^2 $ convex body with positive Gaussian curvature and a circumscribed random polytope with a restricted number of facets, for any probability…

Several years ago the authors started looking at some problems of convex geometry from a more general point of view, replacing volume by an arbitrary measure. This approach led to new general properties of the Radon transform on convex…

We strengthen, in two different ways, the so called Borell-Brascamp- Lieb inequality in the class of power concave functions with compact support. As examples of applications we obtain two quantitative versions of the Brunn- Minkowski…

We prove that on an essentially non-branching $\mathrm{MCP}(K,N)$ space, if a geodesic ball has a volume lower bound and satisfies some additional geometric conditions, then in a smaller geodesic ball (in a quantified sense) we have an…

This note provides a simple proof for the equality between the normalized volume of a convex polytope with $m$ vertices and the mixed volume of $m$ simplices and thus shows the seemingly restrictive problem of computing mixed volume of…

We prove several estimates for the moments of arbitrary measures on convex bodies. We apply these estimates to show a new slicing inequality for measures on convex bodies. We also deduce estimates for the outer volume ratio distance from an…

The use of Bell's theorem in any application or experiment relies on the assumption of free choice or, more precisely, measurement independence, meaning that the measurements can be chosen freely. Here, we prove that even in the simplest…

P\'al's classical isominwidth inequality states that the regular triangle has minimal area among plane convex bodies of minimal width $w$. A similar result is the Blaschke--Lebesgue inequality that states that Reuleaux triangles minimize…

The aim of this work is to formulate two new solutions by decoupling the field equations via a minimal geometric deformation in the context of self-interacting Brans-Dicke gravity. We introduce an extra source in the anisotropic fluid…

We prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same volume bounds the square of the Fraenkel asymmetry of the set.…

We generalize the hyperplane inequality in dimensions up to 4 to the setting of arbitrary measures in place of the volume. To prove this generalization we establish stability in the affirmative part of the solution to the Busemann-Petty…

With Bell's inequalities one has a formal expression to show how essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a simple experimental arrangement. For the case of…

An abstract treatment of Bell inequalities is proposed, in which the parameters characterizing Bell's observable can be times rather than directions. The violation of a Bell inequality might then be taken to mean that a property of a system…

The classical isodiametric inequality in the Euclidean space says that balls maximize the volume among all sets with a given diameter. We consider in this paper the case of Carnot groups. We prove that for any Carnot group equipped with a…