Related papers: Sum rules and large deviations for spectral matrix…
The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…
We consider $n\times n$ Hermitian matrices with i.i.d. entries $X_{ij}$ whose tail probabilities $\mathbb {P}(|X_{ij}|\geq t)$ behave like $e^{-at^{\alpha}}$ for some $a>0$ and $\alpha \in(0,2)$. We establish a large deviation principle for…
It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices. As a…
The consistency of effective models with QCD is investigated through the use of the QCD sum rule. Taking the potential model for the heavy quark system, we apply the method to two phenomenologically successful parameter sets, and obtain the…
Hermite subdivision schemes act on vector valued data that is not only considered as functions values in $\mathbb{R}^r$, but as consecutive derivatives, which leads to a mild form of level dependence of the scheme. Previously, we have…
This paper presents a novel approach to characterize the dynamics of the limit spectrum of large random matrices. This approach is based upon the notion we call "spectral dominance". In particular, we show that the limit spectral measure…
We underline a problem existing in the heavy quark limit of QCD concerning the rates of semileptonic B decays into P-wave $D_J(j)$ mesons, where $j = {1 \over 2}$ (wide states) or $j = {3 \over 2}$ (narrow states). The leading order sum…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
In this paper we study the possibility of generalizing the classical photoabsorption ($\gamma a \to b c$) sum rules, to processes $b c \to \gamma a$ and crossed helicity amplitudes. In the first case, using detailed balance, the sum rule is…
Neutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on…
Borel transformed QCD sum rules conventionally use a real valued parameter (the Borel mass) for specifying the exponential weight over which hadronic spectral functions are averaged. In this paper, it is shown that the Borel mass can be…
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 investigate some QCD corrections that contribute to the Gross-Llewellyn Smith (GLS) sum rule, but have not been included in previous analyses of it. We first review the techniques by which the xF3 structure function is extracted from…
Reconstructive spectrometers are a promising emerging class of devices that combine complex light scattering with inference to enable compact, high-resolution spectrometry. Thus far, the physical determinants of these devices' performance…
In this note we study the right large deviation of the top eigenvalue (or singular value) of the sum or product of two random matrices $\mathbf{A}$ and $\mathbf{B}$ as their dimensions goes to infinity. The matrices $\mathbf{A}$ and…
Let $(X_{jk})_{j,k\geq 1}$ be an infinite array of i.i.d. complex random variables, with mean 0 and variance 1. Let $\la_{n,1},...,\la_{n,n}$ be the eigenvalues of $(\frac{1}{\sqrt{n}}X_{jk})_{1\leq j,k\leq n}$. The strong circular law…
We summarize some recent work on large-Nc sum rules.
It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance matrix $\frac1p XX^T$, where $X$ is a $n\times p$ matrix with independent entries and the distribution function of the…
The aim of this paper is to provide new perspectives on relative finite element accuracy which is usually based on the asymptotic speed of convergence comparison when the mesh size $h$ goes to zero. Starting from a geometrical reading of…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…