Related papers: Finite Free Information Inequalities
Kolmogorov argued that the concept of information exists also in problems with no underlying stochastic model (as Shannon's information representation) for instance, the information contained in an algorithm or in the genome. He introduced…
We consider random trigonometric polynomials with general dependent coefficients. We show that under mild hypotheses on the structure of dependence, the asymptotics as the degree goes to infinity of the expected number of real zeros…
We use techniques from finite free probability to analyze matrix processes related to eigenvalues, singular values, and generalized singular values of random matrices. The models we use are quite basic and the analysis consists entirely of…
We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal…
We study the free product of rooted graphs and its various decompositions using quantum probabilistic methods. We show that the free product of rooted graphs is canonically associated with free independence, which completes the proof of the…
This paper contributes to the current studies on regularity properties of noncommutative distributions in free probability theory. More precisely, we consider evaluations of selfadjoint noncommutative polynomials in noncommutative random…
We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…
We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving…
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…
We study conditional linear information inequalities, i.e., linear inequalities for Shannon entropy that hold for distributions whose entropies meet some linear constraints. We prove that some conditional information inequalities cannot be…
This paper gives an overview about particular quasi-entropies, generalized quantum covariances, quantum Fisher informations, skew-informations and their relations. The point is the dependence on operator monotone functions. It is proven…
We adapt arguments concerning information-theoretic convergence in the Central Limit Theorem to the case of dependent random variables under Rosenblatt mixing conditions. The key is to work with random variables perturbed by the addition of…
Let $\mathbb{K}$ be an algebraically closed field of characteristic zero and let $\mathbb{K}_{C}[[x_{1},...,x_{e}]]$ be the ring of formal power series in several variables with exponents in a line free cone $C$. We consider irreducible…
We consider the problem of approximating all real roots of a square-free polynomial $f$. Given isolating intervals, our algorithm refines each of them to a width of $2^{-L}$ or less, that is, each of the roots is approximated to $L$ bits…
Given a symmetric variety Y defined over the rationals and a non-zero polynomial with integer coefficients, we use techniques from homogeneous dynamics to establish conditions under which the polynomial can be made r-free for a Zariski…
We introduce a new type of Krasnoselskii's result. Using a simple differentiability condition, we relax the nonexpansive condition in Krasnoselskii's theorem. More clearly, we analyze the convergence of the sequence…
Ruzsa's equivalence theorem provided a framework for converting certain families of inequalities in additive combinatorics to entropic inequalities (which sometimes did not possess stand-alone entropic proofs). In this work, we first…
Statements of Shannon's Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the…
The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vall\'ee Poussin filters. These polynomials can be an useful device for many theoretical and…
We introduce a pair of transformations, which are mutually inverse, acting on rather general classes of probability densities in R. These transformations have the property of interchanging the main informational measures such as p-moments,…