Related papers: Sum rules and large deviations for spectral matrix…
Due to its high spatial and spectral information content, hyperspectral imaging opens up new possibilities for a better understanding of data and scenes in a wide variety of applications. An essential part of this process of understanding…
A sum-and-distance system is a collection of finite sets of integers such that the sums and differences formed by taking one element from each set generate a prescribed arithmetic progression. Such systems, with two component sets, arise…
Sum rules among superparticle masses are derived under the assumption that models beyond the MSSM are four-dimensional supersymmetric grand unified theories or five-dimensional supersymmetric orbifold grand unified theories. Sfermion sum…
We study an "inner-product kernel" random matrix model, whose empirical spectral distribution was shown by Xiuyuan Cheng and Amit Singer to converge to a deterministic measure in the large $n$ and $p$ limit. We provide an interpretation of…
The neutrino mixing sum rule $\theta_{12} - \theta_{13}\cos(\delta) \approx \theta^\nu_{12}$ provides a possibility to explore the structure of the neutrino mass matrix in the presence of charged lepton corrections, since it relates the 1-2…
This work is in a stream initiated by a paper of Killip and Simon [Ann. of Math. (2003)]. Using methods of Functional Analysis and the classical Szeg\"o Theorem we prove sum rule identities in a very general form. Then, we apply the result…
We consider the problem of an harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the…
We are going to study the limiting spectral measure of fixed dimensional Hermitian block-matrices with large dimensional Wigner blocks. We are going also to identify the limiting spectral measure when the Hermitian block-structure is…
Assuming the existence of one light sterile neutrino, we investigate the neutrino flavor mixing matrix in matter. Sum rules between the mixing parameters in vacuum and their counterparts in matter are derived. By using these new sum rules,…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
We pursue the idea of assessing chiral restoration via in-medium modifications of hadronic spectral functions of chiral partners. The usefulness of sum rules in this endeavor is illustrated, focusing on the vector and axial-vector channels.…
There is a wide class of models which give a dynamical description of the origin of flavour in terms of spontaneous symmetry breaking of an underlying symmetry. Many of these models exhibit sum rules which relate on the one hand mixing…
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…
Supersymmetric $SO(10)$ grand unified models with renormalizable Yukawa couplings involving only ${\bf 10}$ and $\overline{\bf 126}$ Higgs fields have been shown to realize the fermion masses and mixings economically. In previous works, 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…
New relations between Bjorken polarized, Gross-Llewellyn Smith and Bjorken unpolarized sum rules are proposed. They are based on the ``universality'' of the perturbative and non-perturbative $\rm{1/Q^2}$ contributions to these sum rules.…
A generic physical situation is considered where Im $\Pi$, the imaginary part of polarization operator (generalized susceptibility), can be measured on a finite interval and the high frequency asymptotics (up to a few orders) of $\Pi$ can…
Let $\{{\bf \mathcal{Z}}_n:n\geq 1\}$ be a sequence of i.i.d. random probability measures. Independently, for each $n\geq 1$, let $(X_{n1},\ldots, X_{nn})$ be a random vector of positive random variables that add up to one. This paper…
Gaussian sum-rules, which are related to a two-parameter Gaussian-weighted integral of a hadronic spectral function, are able to examine the possibility that more than one resonance makes a significant contribution to the spectral function.…
Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important…