相关论文: Convergence to Stable Laws in Relative Entropy
A convergent iterative procedure is proposed for the calculation of the relative entropy of entanglement of a given bipartite quantum state. When this state turns out to be non-separable the algorithm provides the corresponding optimal…
A number of inequalities for the weighted entropies is proposed, mirroring properties of a standard (Shannon) entropy and related quantities.
We study some new isoperimetric inequalities on graphs. We etablish a relation between the volume entropy (or asymptotic volume), the systole and the first Betti number of weighted graphs. We also find bounds for the volume, associated to…
Starting from a formulation for the $dS$ element that includes movement, and considering the variation of the entropy Lorentz invariant, we found the relativistic transformations for thermodynamic systems that satisfy the three laws of…
Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional…
New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of $n$ independent random variables to the information contained…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
In this paper homology stability for unitary groups over a ring with finite unitary stable rank is established. Homology stability of symplectic groups and orthogonal groups appears as a special case of our results.
(abbreviated) The statistical mechanics of self-gravitating systems is a long-held puzzle. In this work, we employ a phenomenological entropy form of ideal gas, first proposed by White & Narayan, to revisit this issue. By calculating the…
Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected…
In this paper we consider convergence of approximate solutions of conservation laws. We start with an overview over the historical developments since the 1950s, and the analytical tools used in this context. Then we present some of our own…
Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the…
We formulate conditions for convergence of Laws of Large Numbers and show its links with of the parts of mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of the Law of Large…
Lower bounds for the R\'enyi entropies of sums of independent random variables taking values in cyclic groups of prime order under permutations are established. The main ingredients of our approach are extended rearrangement inequalities in…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
In this work we consider companion conservation laws to general systems of conservation laws. We investigate sufficient regularity for weak solutions to satisfy companion laws, assuming the fluxes to be $C^{1,\gamma}$, $0<\gamma<1$,…
We study a system of several one-dimensional scalar conservation laws coupled through boundary feedback conditions that combine physical boundary constraints with static feedback control laws. Our first contribution establishes the…
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.
The relative entropy in two-dimensional Field Theory is studied for its application as an irreversible quantity under the Renormalization Group, relying on a general monotonicity theorem for that quantity previously established. In the…
We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…