Related papers: On some inequalities for Gaussian measures

We extend a Gaussian functional inequality to a countable product of Gaussian measures. This inequality improves on the classical Poincare inequality for Gaussian measures. As an application, we prove that First Passage Percolation has…

In this article, we explore the celebrated Gr\"{u}ss inequality, where we present a new approach using the Gr\"{u}ss inequality to obtain new refinements of operator means inequalities. We also present several operator Gr\"{u}ss-type…

In a 2013 paper, the author showed that the convolution of a compactly supported measure on the real line with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). In a 2014 paper, the author gave bounds for the optimal…

There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…

We study coercive inequalities on finite dimensional metric spaces with probability measures which do not have volume doubling property. This class of inequalities includes Poincar\'e and Log-Sobolev inequality. Our main result is proof of…

In this paper, we prove some isoperimetric inequalities and give a sharp bound for the positive solution of sublinear elliptic equations.

We extend the classical Lyapunov inequality on the measurable space with infinite measure and on the so-called Grand Lebesgue spaces (GLS). We find also the exact value for correspondent constant. Possible applications: Functional Analysis…

We consider geometrical optimization problems related to optimizing the error probability in the presence of a Gaussian noise. One famous questions in the field is the "weak simplex conjecture". We discuss possible approaches to it, and…

We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio…

We prove quasi-invariance of Gaussian measures supported on Sobolev spaces under the dynamics of the three-dimensional defocusing cubic nonlinear wave equation. As in the previous work on the two-dimensional case, we employ a simultaneous…

In this survey we consider generalizations for Young and Cauchy--Bunyakowsky inequalities with applications.

We investigate the Plateau and isoperimetric problems associated to Fefferman's measure for strongly pseudoconvex real hypersurfaces in $\mathbb C^n$ (focusing on the case $n=2$), showing in particular that the isoperimetric problem shares…

The aim of this paper is to establish various functional inequalities for the convolution of a compactly supported measure and a standard Gaussian distribution on Rd. We especially focus on getting good dependence of the constants on the…

New isoperimetric inequalities for lower order eigenvalues of the Laplacian on closed hypersurfaces, of the biharmonic Steklov problems and of the Wentzell-Laplace on bounded domains in a Euclidean space are proven. Some open questions for…

Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…

On fractals, different measures (mutually singular in general) are involved to measure volumes of sets and energies of functions. Singularity of measures brings difficulties in (especially non-linear) analysis on fractals. In this paper, we…

In this expository paper, we discuss a unified framework for proving various geometric inequalities, based on the so-called Alexandrov-Bakelman-Pucci technique. Examples include Cabr\'e's proof of the classical isoperimetric inequality in…

We discuss general Bell inequalities for bipartite and multipartite systems, emphasizing the connection with convex geometry on the mathematical side, and the communication aspects on the physical side. Known results on families of…

Bell inequalities are a consequence of measurement incompatibility (not, as generally thought, of nonlocality). In classical terms, this is equivalent to contextuality -- measurement devices do have a significant effect. Contextual models…