Related papers: On Relations Between the Relative entropy and $\ch…
Consider the likelihood ratio test (LRT) statistics for the independence of sub-vectors from a $p$-variate normal random vector. We are devoted to deriving the limiting distributions of the LRT statistics based on a random sample of size…
Statistical depth, which measures the center-outward rank of a given sample with respect to its underlying distribution, has become a popular and powerful tool in nonparametric inference. In this paper, we investigate the use of statistical…
In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…
We introduce the concept of \textit{defect relative entropy} as a measure of distinguishability within the space of defects. We compute the defect relative entropy for conformal/topological defects, deriving a universal formula in conformal…
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent…
This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…
Exponential convergence rates in the $L^2$-tail norm and entropy are characterized for the second quantization semigroups by using the corresponding base Dirichlet form. This supplements the well known result on the $L^2$-exponential…
Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated, i.e. disassortative? With a view to answering this long-standing question, we define a general class of degree-degree…
Divergences are quantities that measure discrepancy between two probability distributions and play an important role in various fields such as statistics and machine learning. Divergences are non-negative and are equal to zero if and only…
We show that under natural growth conditions on the entropy function, convergence in relative entropy is equivalent to $L_p$-convergence. The main tool is the theory of Young measures, in a form that accounts for the formation of…
Strong data processing inequalities (SDPI) are an important object of study in Information Theory and have been well studied for $f$-divergences. Universal upper and lower bounds have been provided along with several applications,…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
We study the R\'enyi entropy and subsystem distances on one interval for the finite size and thermal states in the critical XY chains, focusing on the critical Ising chain and XX chain with zero transverse field. We construct numerically…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
Fidelity and relative entropy are two significant quantities in quantum information theory. We study the quantum fidelity and relative entropy under unitary orbits. The maximal and minimal quantum fidelity and relative entropy between two…