Related papers: Asymptotic Expansions of Smooth R\'{e}nyi Entropie…
One-shot information theory entertains a plethora of entropic quantities, such as the smooth max-divergence, hypothesis testing divergence and information spectrum divergence, that characterize various operational tasks and are used to…
The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions…
A method is presented for computing the R\'enyi entropy of a perturbed massless vacuum on the ball via a comparison with lattice field theory. If the perturbed state is Gaussian with smoothly varying correlation functions and the…
We propose a new asymptotic expansion method for nonlinear filtering, based on a small parameter in the system noise. The conditional expectation is expanded as a power series in the noise level, with each coefficient computed by solving a…
Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
We study the problem of discovering the simplest latent variable that can make two observed discrete variables conditionally independent. The minimum entropy required for such a latent is known as common entropy in information theory. We…
Shannon's entropy is one of the building blocks of information theory and an essential aspect of Machine Learning methods (e.g., Random Forests). Yet, it is only finitely defined for distributions with fast decaying tails on a countable…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
In this paper, we derive the early-time asymptotics for fixed-frequency solutions $\phi_\ell$ to the wave equation $\Box_g \phi_\ell=0$ on a fixed Schwarzschild background ($M>0$) arising from the no incoming radiation condition on…
One-shot achievable rate region for source coding when coded side information is available at the decoder (source coding with a helper) is proposed. The achievable region proposed is in terms of conditional smooth max Renyi entropy and…
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…
The entanglement entropy in many gapless quantum systems receives a contribution from corners in the entangling surface in 2+1d. It is characterized by a universal function $a(\theta)$ depending on the opening angle $\theta$, and contains…
Quantum processes can exhibit scenarios beyond a fixed order of events. We propose information inequalities that, when violated, constitute sufficient conditions to certify quantum processes without a fixed causal order -- causally…
We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require only uniform boundedness of the cost function and no…
We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of $\alpha$-R\'{e}nyi relative entropy. We develop a unifying treatment towards the improvement of some quantum entropy inequalities. In…
The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic R\'enyi…
There is a vast body of recent literature on the reliability of communication through noisy channels, the recovery of community structures in the stochastic block model, the limiting behavior of the free entropy in spin glasses and the…
Recently, there has been renewed interest in studying the asymptotic properties of the integer partition function $p(n)$. Hardy, Ramanujan, and Rademacher provided detailed asymptotic analysis for $p(n)$. Presently, attention has shifted…