Related papers: Strong Linear Correlation Between Eigenvalues and …
Ultracold interacting atoms are an excellent tool to study correlation functions of many-body systems that are generally eluding detection and manipulation. Herein, we investigate the ground state of bosons in a tilted triple-well potential…
The distributions of the smallest and largest eigenvalues for the matrix product $Z^\dagger Z$, where $Z$ is an $n \times m$ complex Gaussian matrix with correlations both along rows and down columns, are expressed as $m \times m$…
We show how coherences between identical constituents of a many-body quantum state can be interrogated by suitable correlation functions, and identify sufficient conditions under which low-order correlators fully characterize many-body…
In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue…
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of…
We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer…
Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of…
We compute the asymptotic empirical eigenvalue distribution of the matrix $M = \bigodot_{i=1}^k \frac{1}{d_i}X^{(i)}{X^{(i)}}^\top$ where $X^{(i)}\in\mathbb{R}^{n\times d_i}$ are independent matrices with independent rows but general…
This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…
We show that the last few components in principal component analysis of the correlation matrix of a group of stocks may contain useful financial information by identifying highly correlated pairs or larger groups of stocks. The results of…
The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…
Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered…
We consider a specific form of explicitly correlated Gaussians -- with tensor pre-factors -- which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these…
We analytically compute the large-deviation probability of a diagonal matrix element of two cases of random matrices, namely $\beta=[\vec H^\dagger\vec H]^{-1}_{11}$ and $\gamma=[\vec I_N+\rho\vec H^\dagger\vec H]^{-1}_{11}$, where $\vec H$…
Recent applications in queuing theory and statistical mechanics have isolated the process formed by the eigenvalues of successive minors of the GUE. Analogous eigenvalue processes, formed in general from the eigenvalues of nested sequences…
We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small off-diagonal elements…
The study of correlated time-series is ubiquitous in statistical analysis, and the matrix decomposition of the cross-correlations between time series is a universal tool to extract the principal patterns of behavior in a wide range of…
One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants…
We continue here to study simple matrix models of quantum mechanical Hamiltonians. The eigenvalues and eigenfunctions were associated energy levels and wave functions. Whereas previously we considered the weak coupling limits of our models,…
Charged soft-matter systems--such as colloidal dispersions and charged polymers--are dominated by attractive forces between constituent like-charged particles when neutralizing counterions of high charge valency are introduced. Such…