相关论文: Asymptotic behavior of R\'enyi entropy in the cent…

We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.

The paper extends the analysis of the entropies of the Poisson distribution with parameter $\lambda$. It demonstrates that the Tsallis and Sharma-Mittal entropies exhibit monotonic behavior with respect to $\lambda$, whereas two generalized…

We introduce asymptotic R\'enyi entropies as a parameterized family of invariants for random walks on groups. These invariants interpolate between various well-studied properties of the random walk, including the growth rate of the group,…

This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…

We study R\'enyi entropy of locally excited states with considering the thermal and boundary effects respectively in two dimensional conformal field theories (CFTs). Firstly we consider locally excited states obtained by acting primary…

We show that a recent definition of relative R\'enyi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of M\"uller-Lennert et al.

In this paper, we first investigate the monotonicity and limit problem of the fractional integral functions. By fixed point theorem and these new results of the fractional integral functions, we present that the Riemann-Liouville fractional…

We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.

We present some new nonparametric estimators of entropies and we establish almost sure consistency and central limit Theorems for some of the most important entropies in the discrete case. Our theorical results are validated by simulations.

The von Neumann entropy of a density matrix of dimension d, expressed in terms of the first d-1 integer order R\'enyi entropies, is monotonically increasing in R\'enyi entropies of even order and decreasing in those of odd order.

We investigate the large-time asymptotics of nonlinear diffusion equations $u_t = \Delta u^p$ in dimension $n \ge 1$, in the exponent interval $p > n/(n+2)$, when the initial datum $u_0$ is of bounded second moment. Precise rates of…

We study the distribution of the order of a random permutation of $[n]$ through the lens of R\'enyi entropy. In particular, we obtain an asymptotic for the R\'enyi $q$-entropy of the order in the full range $1 \leq q \leq \infty$. For $q >…

In this paper we consider convergence of moments in the small-time limit theorems for L\'evy processes. We provide precise asymptotics for all the absolute moments of positive order. The convergence of moments in limit theorems holds…

We compute R\'enyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two-dimensional quantum systems. The relative amount of uncertainty between two states depends on the uncertainty…

R\'enyi entropies are conceptually valuable and experimentally relevant generalisations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal…

We extend Bobkov and Chistyakov's (2015) upper bounds on concentration functions of sums of independent random variables to a multivariate entropic setting. The approach is based on pointwise estimates on densities of sums of independent…

Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…

We study the central limit theorem in the non-normal domain of attraction to symmetric $\alpha$-stable laws for $0<\alpha\leq2$. We show that for i.i.d. random variables $X_i$, the convergence rate in $L^\infty$ of both the densities and…

In this paper, we investigate the complete monotonicity of R\'enyi entropy along the heat flow. We confirm this property for the order of derivative up to $4$, when the order of R\'enyi entropy is in certain regimes. We also investigate…

This paper investigates the problem of guessing subject to distortion, which was introduced by Arikan and Merhav. While the primary concern of the previous study was asymptotic analysis, our primary concern is non-asymptotic analysis. We…