Related papers: The distribution of density matrices at fixed puri…

A cornerstone of current-density functional theory (CDFT) in its paramagnetic formulation is proven. After a brief outline of the mathematical structure of CDFT, the lower semi-continuity and expectation valuedness of the CDFT…

The need to immobilize low-level nuclear waste, in particular 137Cs-bearing waste, has led to a growing interest in geopolymer-based waste matrices, in addition to optimization attempts of cement matrix compositions for this specific…

The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that representing instead the $\mathit{logarithm}$ of the density…

The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF),…

Consider the random matrix $\Sigma = D^{1/2} X \widetilde D^{1/2}$ where $D$ and $\widetilde D$ are deterministic Hermitian nonnegative matrices with respective dimensions $N \times N$ and $n \times n$, and where $X$ is a random matrix with…

We discuss the product of $M$ rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint…

Random matrix models consisting of normal matrices, defined by the sole constraint $[N^{\dag},N]=0$, will be explored. It is shown that cubic eigenvalue repulsion in the complex plane is universal with respect to the probability…

Eigenvalues of a density matrix characterize well the quantum state's properties, such as coherence and entanglement. We propose a simple method to determine all the eigenvalues of an unknown density matrix of a finite-dimensional system in…

We compute individual distributions of low-lying eigenvalues of massive chiral random matrix ensembles by the Nystr\"om-type quadrature method for evaluating the Fredholm determinant and Pfaffian that represent the analytic continuation of…

Density functional theory (DFT), one of the most widely utilized methods available to computational chemistry, fails to describe systems with statically correlated electrons. To address this shortcoming, in previous work we transformed DFT…

Density functional theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically…

We provide a general formula for the eigenvalue density of large random $N\times N$ matrices of the form $A = M + LJR$, where $M$, $L$ and $R$ are arbitrary deterministic matrices and $J$ is a random matrix of zero-mean independent and…

In this work we study the spectral density of products of Wishart diluted random matrices of the form $X(1)\cdots X(M)(X(1)\cdots X(M))^T$ using the Edwards-Jones trick to map this problem into a system of interacting particles with random…

Let $f(n)$ be a Steinhaus random multiplicative function. Let $A\subset [1, N]$ be a finite set of integers. We show that \[\frac{1}{\sqrt{|A|}} \sum_{n\in A} f(n) \xrightarrow[]{d} \mathcal{CN}(0,1)\] forces that $|A|=o(N)$. We prove that…

Let $ X_{n} $ be $ n\times N $ random complex matrices, $R_{n}$ and $T_{n}$ be non-random complex matrices with dimensions $n\times N$ and $n\times n$, respectively. We assume that the entries of $ X_{n} $ are independent and identically…

Using an analytic model calibrated against numerical simulations, we calculate the central densities of dark matter halos in a ``conventional'' cold dark matter model with a cosmological constant (LCDM) and in a ``tilted'' model (TLCDM)…

The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the…

The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field…

We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…

Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely…