相关论文: Combinatorial Entropy Power Inequalities: A Prelim…
The entropy region is constructed from vectors of random variables by collecting Shannon entropies of all subvectors. Its shape is studied here by means of polymatroidal constructions, notably by convolution. The closure of the region is…
The region of entropic vectors is a convex cone that has been shown to be at the core of many fundamental limits for problems in multiterminal data compression, network coding, and multimedia transmission. This cone has been shown to be…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…
Given n (discrete or continuous) random variables X_i, the (2^n-1)-dimensional vector obtained by evaluating the joint entropy of all non-empty subsets of {X_1,...,X_n} is called an entropic vector. Determining the region of entropic…
The entropy region is a fundamental object in information theory. An outer bound for the entropy region is defined by a minimal set of Shannon-type inequalities called elemental inequalities also referred to as the Shannon region. This…
We introduce a novel concept of rank for subsets of finite metric spaces E^n_q (the set of all n-dimensional vectors over an alphabet of size q) equipped with the Hamming distance, where the rank R(A) of a subset A is defined as the number…
We tighten the Entropy Power Inequality (EPI) when one of the random summands is Gaussian. Our strengthening is closely connected to the concept of strong data processing for Gaussian channels and generalizes the (vector extension of)…
The entropic region is formed by the collection of the Shannon entropies of all subvectors of finitely many jointly distributed discrete random variables. For four or more variables, the structure of the entropic region is mostly unknown.…
In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…
We study the local non-extendability of random power series beyond their disk of convergence. We show that random power series formed by independent coefficients which are asymptotically anti-concentrated admit the circle of radius of…
We consider the set of the power non-negative polynomials of several variables and its subset that consists of polynomials which can be represented as a sum of squares. It is shown in the classic work by D.Hilbert that it is a proper…
Over the past few years, a family of interesting new inequalities for the entropies of sums and differences of random variables has been developed by Ruzsa, Tao and others, motivated by analogous results in additive combinatorics. The…
A lower bound on the R\'enyi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the…
We find a sharp combinatorial bound for the metric entropy of sets in R^n and general classes of functions. This solves two basic combinatorial conjectures on the empirical processes. 1. A class of functions satisfies the uniform Central…
The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not…
Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…
We introduce a new measure of interdependence among the components of a random vector along the main diagonal of the vector copula, i.e. along the line $u_{1}=\ldots=u_{J}$, for $\left(u_{1},\ldots,u_{J}\right)\in\left[0,1\right]^{J}$. Our…
As was shown recently by the authors, the entropy power inequality can be reversed for independent summands with sufficiently concave densities, when the distributions of the summands are put in a special position. In this note it is proved…
We consider an intrinsic entropy associated with a local conformal net A by the coefficients in the expansion of the logarithm of the trace of the ``heat kernel'' semigroup. In analogy with Weyl theorem on the asymptotic density…
We study entanglement properties of systems with spontaneously broken continuous symmetry. We find that in addition to the expected area law behavior, the entanglement entropy contains a subleading contribution which diverges…