Related papers: The case for shifting the Renyi Entropy
Using a sharp version of the reverse Young inequality, and a R\'enyi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive R\'enyi entropy power inequalities for log-concave random vectors when…
We show how entanglement entropies allow for the estimation of quasi-long-range order in one dimensional systems whose low-energy physics is well captured by the Tomonaga-Luttinger liquid universality class. First, we check our procedure in…
Shannon and Renyi entropies are quantitative measures of uncertainty in a data set. They are developed by Renyi in the context of entropy theory. These measures have been studied in the case of the multivariate t-distributions. We extend…
Conventional information-theoretic quantities assume access to probability distributions. Estimating such distributions is not trivial. Here, we consider function-based formulations of cross entropy that sidesteps this a priori estimation…
The exact range of the joined values of several R\'{e}nyi entropies is determined. The method is based on topology with special emphasis on the orientation of the objects studied. Like in the case when only two orders of R\'{e}nyi entropies…
Starting from the geometrical interpretation of the R\'enyi entropy, we introduce further extensive generalizations and study their properties. In particular, we found the probability distribution function obtained by the MaxEnt principle…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
It was recently shown that estimating the Shannon entropy $H({\rm p})$ of a discrete $k$-symbol distribution ${\rm p}$ requires $\Theta(k/\log k)$ samples, a number that grows near-linearly in the support size. In many applications $H({\rm…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
The matrix-based Renyi's \alpha-order entropy functional was recently introduced using the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the current theory in the…
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
The matrix-based R\'enyi's entropy allows us to directly quantify information measures from given data, without explicit estimation of the underlying probability distribution. This intriguing property makes it widely applied in statistical…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of…
We prove R\'enyi entropic inequalities in a holographic setup based on the recent proposal for the holographic formula of R\'enyi entropies when the bulk is stable against any perturbation. Regarding the R\'enyi parameter as an inverse…
We calculate analytically the Renyi entropy for the zeta-urn model with a Gibbs measure definition of the micro-state probabilities. This allows us to obtain the singularities in the R\'enyi entropy from those of the thermodynamic…
We discuss the interest of escort distributions and R\'enyi entropy in the context of source coding. We first recall a source coding theorem by Campbell relating a generalized measure of length to the R\'enyi-Tsallis entropy. We show that…
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…