Related papers: Gaussian Correlation Conjecture for Symmetric Conv…

Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…

We show that for a fixed amount of entanglement, two-mode squeezed states are those that maximize Einstein-Podolsky-Rosen-like correlations. We use this fact to determine the entanglement of formation for all symmetric Gaussian states…

We discuss connections between certain well-known open problems related to the uniform measure on a high-dimensional convex body. In particular, we show that the "thin shell conjecture" implies the "hyperplane conjecture". This extends a…

We quantify correlations (quantum and/or classical) between two continuous variable modes in terms of how many correlated bits can be extracted by measuring the sign of two local quadratures. On Gaussian states, such `bit quadrature…

This article contains a survey of the geometric approach to quantum correlations. We focus mainly on the geometric measures of quantum correlations based on the Bures and quantum Hellinger distances.

Several results about the union-closed sets conjecture are presented.

A method is proposed that allows one to infer the sum of the values of an observable taken during contacts with a pointer state. Hereby the state of the pointer is updated while contacted with the system and remains unchanged between…

Gaussian blur is a commonly-used method to filter image data. This paper introduces the collapsing sum, a new operator on matrices that provides a combinatorial interpretation of Gaussian blur. We study the combinatorial properties of this…

Total correlation (`TC') and dual total correlation (`DTC') are two classical ways to quantify the correlation among an $n$-tuple of random variables. They both reduce to mutual information when $n=2$. The first part of this paper sets up…

Context. Whenever correlation functions are used for inference about cosmological parameters in the context of a Bayesian analysis, the likelihood function of correlation functions needs to be known. Usually, it is approximated as a…

We introduce a new notion of influence for symmetric convex sets over Gaussian space, which we term "convex influence". We show that this new notion of influence shares many of the familiar properties of influences of variables for monotone…

The Gaussian unitary random matrix ensembles satisfying some additional symmetry conditions are considered. The effect of these conditions on the limiting normalized counting measures and correlation functions is studied.

In this paper we study the functional given by the integral of the mean curvature of a convex set with Gaussian weight with Gaussian volume constraint. It was conjectured that the ball centered at the origin is the only minimizer of such a…

We prove that every pointed closed convex set in $\mathbb{R}^n$ is the intersection of all the rational closed halfspaces that contain it. This generalizes a previous result by the authors for compact convex sets.

The verification and quantification of experimentally created entanglement by simple measurements, especially between distant particles, is an important basic task in quantum processing. When composite systems are subjected to local…

The quantumness of the correlation known as quantum correlation is usually measured by quantum discord. So far various quantum discords can be roughly understood as indirect measure by some special discrepancy of two quantities. We present…

The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…

We consider the problem of predicting the covariance of a zero mean Gaussian vector, based on another feature vector. We describe a covariance predictor that has the form of a generalized linear model, i.e., an affine function of the…

In this paper, we prove a theorem that gives a simple criterion for generating commuting pairs of generalized almost complex structures on spaces that are the product of two generalized almost contact metric spaces. We examine the…

Convex analysis and Gaussian probability are tightly connected, as mostly evident in the theory of linear regression. Our work introduces an algebraic perspective on such relationship, in the form of a diagrammatic calculus of string…