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Laplacian matrices are commonly employed in many real applications, encoding the underlying latent structural information such as graphs and manifolds. The use of the normalization terms naturally gives rise to random matrices with…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
Two-parameter perturbation theory (2PPT) is a framework designed to include the relativistic gravitational effects of small-scale nonlinear structures on the large-scale properties of the Universe. In this paper we use the 2PPT framework to…
In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the…
Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimension of very high-dimensional tensors. Following the work in [30], we consider a tensorized random…
We propose a novel statistical approach to the analysis of experimental data obtained in nucleus-nucleus collisions at high energies which borrows from methods developed within the context of Random Matrix Theory. It is applied to the…
The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic…
We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems beyond the ground state. Various obstacles which historically have doomed such an…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamical…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
We perform a Random Matrix Theory (RMT) analysis of the quantum four-state chiral Potts chain for different sizes of the chain up to size L=8. Our analysis gives clear evidence of a Gaussian Orthogonal Ensemble statistics, suggesting the…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
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 propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…
The statistical distribution of levels of an integrable system is claimed to be a Poisson distribution. In this paper, we numerically generate an ensemble of N dimensional random diagonal matrices as a model for regular systems. We evaluate…
We introduce a theory of probability in $\lambda$-rings designed to efficiently describe random variables valued in multisets of complex numbers, varieties over a field, or other similar enriched settings. A key role is played by the…
We show that spectral fluctuation of interaction matrices of yeast a core protein interaction network and a metabolic network follows the description of the Gaussian orthogonal ensemble (GOE) of random matrix theory (RMT). Furthermore, we…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…
We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…