Related papers: Convergence to Stable Laws in Relative Entropy
Previously proposed measures of entanglement, such as entanglement of formation and assistance, are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is…
We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional…
A lower bound of the reduced relative entropy is given by the use of a variational expression. The reduced Tsallis relative entropy is defined and some results are given. In particular, the convexity of the reduced Tsallis relative entropy…
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an…
We introduce a new generalization of relative entropy to non-negative vectors with sums $\gt 1$. We show in a purely combinatorial setting, with no probabilistic considerations, that in the presence of linear constraints defining a convex…
Stable laws can be tempered by modifying the L\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk…
We develop a general framework for the analysis of approximations to stochastic scalar conservation laws. Our aim is to prove, under minimal consistency properties and bounds, that such approximations are converging to the solution to a…
We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.
The second law of thermodynamics is discussed and reformulated from a quantum information theoretic perspective for open quantum systems using relative entropy. Specifically, the relative entropy of a quantum state with respect to…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…
This work revisits a recent finding by the first author concerning the local convergence of a regularized scalar conservation law. We significantly improve the original statement by establishing a global convergence result within the…
Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is…
We provide a thorough study of stability of the 1-D continuity equation, which models many physical conservation laws. In our system-theoretic perspective, the velocity is considered to be an input. An additional input appears in the…
We study generically stable types/measures in both classical and continuous logics, and their connection with randomization and modes of convergence of types/measures.
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…
In [1], Collins et al. showed that the quantum entropy of random graph states satisfies the so-called area law as the local dimension tends to be large. In this paper, we continue to study the fluctuation of the convergence and thus prove…
An "entropy increasing to the maximum" result analogous to the entropic central limit theorem (Barron 1986; Artstein et al. 2004) is obtained in the discrete setting. This involves the thinning operation and a Poisson limit. Monotonic…
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.