Related papers: Exact eigenvalue order statistics for the reduced …
The second-order reduced density matrix method (the RDM method) has performed well in determining energies and properties of atomic and molecular systems, achieving coupled-cluster singles and doubles with perturbative triples (CC SD(T))…
We compute the full order statistics of a one-dimensional gas of fermions in a harmonic trap at zero temperature, including its large deviation tails. The problem amounts to computing the probability distribution of the $k$th smallest…
In this paper we construct a class of random matrix ensembles labelled by a real parameter $\alpha \in (0,1)$, whose eigenvalue density near zero behaves like $|x|^\alpha$. The eigenvalue spacing near zero scales like $1/N^{1/(1+\alpha)}$…
We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the…
In this paper we discuss reduced order models for the approximation of parametric eigenvalue problems. In particular, we are interested in the presence of intersections or clusters of eigenvalues. The singularities originating by these…
A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk. This is also true for a product $P_m$ of $m$…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
In this article we consider products of real random matrices with fixed size. Let $A_1,A_2, \dots $ be i.i.d $k \times k$ real matrices, whose entries are independent and identically distributed from probability measure $\mu$. Let $X_n =…
Let $\boldsymbol{\Sigma}_N$ be a $M \times N$ random matrix defined by $\boldsymbol{\Sigma}_N = \mathbf{B}_N + \sigma \mathbf{W}_N$ where $\mathbf{B}_N$ is a uniformly bounded deterministic matrix and where $\mathbf{W}_N$ is an independent…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
Classical random matrix ensembles with orthogonal symmetry have the property that the joint distribution of every second eigenvalue is equal to that of a classical random matrix ensemble with symplectic symmetry. These results are shown to…
We suggest a method of studying the joint probability density (JPD) of an eigenvalue and the associated 'non-orthogonality overlap factor' (also known as the 'eigenvalue condition number') of the left and right eigenvectors for…
We study the problem of bivariate discrete or continuous probability density estimation under low-rank constraints.For discrete distributions, we assume that the two-dimensional array to estimate is a low-rank probability matrix. In the…
The zeros of complex Gaussian random polynomials, with coefficients such that the density in the underlying complex space is uniform, are known to have the same statistical properties as the zeros of the coherent state representation of…
This paper is concerned with computations of a few smaller eigenvalues (in absolute value) of a large extremely ill-conditioned matrix. It is shown that smaller eigenvalues can be accurately computed for a diagonally dominant matrix or a…
Determining whether two particle systems are similar is a common problem in particle simulations. When the comparison should be invariant under permutations, orthogonal transformations, and translations of the systems, special techniques…
We investigate the structure of the one-body Reduced Density Matrix (1RDM) of three electron systems, i.e. doublet and quadruplet spin configurations, corresponding to the smallest interacting system with an open-shell ground state. To this…
We consider extremal eigenvalues of sparse random matrices, a class of random matrices including the adjacency matrices of Erd\H{o}s-R\'{e}nyi graphs $\mathcal{G}(N,p)$. Recently, it was shown that the leading order fluctuations of extremal…
We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The…
We propose and study an algorithm for computing a nearest passive system to a given non-passive linear time-invariant system (with much freedom in the choice of the metric defining `nearest', which may be restricted to structured…