Related papers: Sum rules via large deviations: extension to polyn…
A new technique based on H\"older's integral inequality is applied to QCD sum-rules to provide fundamental constraints on the sum-rule parameters. These constraints must be satisfied if the sum-rules are to consistently describe integrated…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
We derive a sum rule which establishes a linear relation between a particle's anomalous magnetic moment and a quantity connected to the photoabsorption cross-section. This quantity cannot be measured directly. However, it can be computed…
By incorporating contributions from both the (chromo)electric scale $gT$ and (chromo)magnetic scale $g^2T$, we establish spectral sum rules of quarks for strongly coupled QCD that respect Fermi-Dirac statistics as required by quantum…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
Scoring rules measure the deviation between a probabilistic forecast and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is…
We define a function of two real vectors by a certain homogeneous quotient involving power sums, and show that its supremum grows asymptotically linearly w.r.t. the dimension. From this, we deduce a condition under which a parametric set of…
Concerning systematic effects, the recommendation given in the GUM is to correct for them, but unfortunately no detailed information is available, how to do this. This publication will show, how systematic measurement deviations can be…
We propose a sum rule for derangements. Three different proofs are provided. The first one involves integral representations and the second one relies on the Hermite identity for the integer part of the product of an integer by a real…
We introduce an algebra model to study higher order sum rules for orthogonal polynomials on the unit circle. We build the relation between the algebra model and sum rules, and prove an equivalent expression on the algebra side for the sum…
We establish a set of exact sum rules that relate the interatomic force constants to the frequency-dependent electromagnetic susceptibility of a solid or molecule, thereby generalizing the long-established principles of rototranslational…
The theory of large deviations constitutes a mathematical cornerstone in the foundations of Boltzmann-Gibbs statistical mechanics, based on the additive entropy $S_{BG}=- k_B\sum_{i=1}^W p_i \ln p_i$. Its optimization under appropriate…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…
We construct a multi-observable uncertainty equality as well as an inequality based on the sum of standard deviations in the qubit system. The obtained equality indicates that the uncertainty relation can be expressed more accurately, and…
One of the main features of eigenvalue matrix models is that the averages of characters are again characters, what can be considered as a far-going generalization of the Fourier transform property of Gaussian exponential. This is true for…
We consider the differential sum rule for the effective scattering rate $% 1/\tau (\omega)$ and optical conductivity $\sigma_{1}(\omega) $ in a dirty BCS superconductor, for arbitrary ratio of the superconducting gap $% \Delta$ and the…
In connection with recent publications we discuss spectral sum rules for the Tomonaga-Luttinger model without using the explicit result for the one-electron Green's function. They are usefull in the interpretation of recent high resolution…
The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…
We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time…