Related papers: Sum rules via large deviations: polynomial potenti…
Different decompositions (sum rules) for the proton mass have been proposed in the literature. All of them are related to the energy-momentum tensor in quantum chromodynamics. We review and revisit these decompositions by paying special…
Systems of orthogonal polynomials whose recurrence coefficients tend to infinity are considered. A summability condition is imposed on the coefficients and the consequences for the measure of orthogonality are discussed. Also discussed are…
The reduction of constraints to obtain minimal representations of sets is a very common problem in many engineering applications. While well-established methodologies exist for the case of linear constraints, the problem of how to detect…
In this note we report about a method to deal with finite energy sum rules. With a reasonable knowledge of the main resonances of the spectrum, the method guarantees that we can find a nice duality matching between the low energy hadronic…
We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…
A correlation function of two particles with small relative velocities obeys a sum rule - the momentum integral of the function is determined due to the completeness of quantum states of the particles. The original sum rule derived in 1995…
We show a simple method for constructing larger matrices but preserving the spectral radius. This yields a sufficient criteria for two square matrices of arbitrary dimension have the same spectral radius, a way to compare spectral radii of…
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…
QCD sum rules are useful tools for studying the spectral properties of hadrons; however, assumptions underlying standard sum-rule analyses can lead to inconsistencies with known results of chiral perturbation theory. This possibility is…
We compare among themselves two different methods for the derivation of results following from the requirement of polynomial boundedness of tree-level chiral amplitudes. It is shown that the results of the algebraic approach are valid also…
A new approach of the QCD sum rule is proposed in which positive and negative-parity baryons couple with each other. With positive and negative-parity states explicitly taken into account, sum rules are derived by means of the dispersion…
Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices…
The Gerasimov-Drell-Hearn sum rule and related dispersive integrals connect real and virtual Compton scattering to inclusive photo- and electroproduction. Being based on universal principles as causality, unitarity, and gauge invariance,…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Sum rules are derived relating mean squared charge radii of the pseudoscalar mesons with the convergent integral of the difference of hadron photoproduction cross-sections on pseudoscalar mesons.
The circular uniform distribution on the unit circle is closed under summation, that is, the sum of independent circular uniformly distributed random variables is also circular uniformly distributed. In this study, it is shown that a family…
We discuss the extraction of ground-state parameters, such as decay constants and form factors, from two- and three-point dispersive sum rules, making use of a quantum-mechanical potential model. This model provides a unique possibility to…
A system of biorthogonal polynomials with respect to a complex valued measure supported on the unit circle is considered and all the terms with bounds are explicitly given for the remainder of an asymptotic formula given by R. Askey for…
In this paper, we establish a new law of large numbers with the rate of convergence for special partial sums in a probability space. The proof relies on nonlinear expectation theory, as the uncertainty of random variables in the special…
We describe the results of our recent work on the determination of the value of the parameter $\Lambda_{\overline{MS}}^{(4)}$ and of the $Q^2$-dependence of the Gross--Llewellyn Smith (GLS) sum rule from the experimental data of the CCFR…