Related papers: Random-Matrix Approach to RPA equations. I
This paper investigates the spectral properties of spatial-sign covariance matrices, a self-normalized version of sample covariance matrices, for data from $\alpha$-regularly varying populations with general covariance structures. By…
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…
Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture…
The matrix equations of the relativistic random-phase approximation (RRPA) are derived for an effective Lagrangian characterized by density-dependent meson-nucleon vertex functions. The explicit density dependence of the meson-nucleon…
To reduce peak-to-average power ratio, we propose a method to choose a suitable vector for a partial transmit sequence technique. With a conventional method for this technique, we have to choose a suitable vector from a large amount of…
In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the…
We bring together three key amplification mechanisms in linear dynamical systems: spectral criticality, resonance, and non-normality. We present a unified linear framework that both distinguishes and quantitatively links these effects…
Recently, it became possible to experimentally generate and characterize a very thin silica system on a substrate which can be basically described as a 2D random network. The key structural properties, in particular related to the ring…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
We present a simple, perturbative approach for calculating spectral densities for random matrix ensembles in the thermodynamic limit we call the Perturbative Resolvent Method (PRM). The PRM is based on constructing a linear system of…
Computing the agreement between two continuous sequences is of great interest in statistics when comparing two instruments or one instrument with a gold standard. The probability of agreement (PA) quantifies the similarity between two…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
In this paper, we investigate the testing problem that the spectral density matrices of several, not necessarily independent, stationary processes are equal. Based on an $L_2$-type test statistic, we propose a new nonparametric approach,…
This paper introduces and analyses a general statistical model, termed the RARE model, of random relaxation processes in disordered systems. The model considers excitations, that are randomly scattered around a reaction center in a general…
One of the main tasks for present and future dark energy surveys is to determine whether the dark energy is dynamical or not. To illustrate this from data, it is commonly used to parameterize the dark energy equation of state w as several…
In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and…
This paper considers the phenomenon of distinct regional frequencies recently observed in some power systems. First, a reduced-order mathematical model describing this behaviour is developed. Then, techniques to solve the model are…