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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…
Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…
We study the spectral norm of random kernel matrices with polynomial scaling, where the number of samples scales polynomially with the data dimension. In this regime, Lu and Yau (2022) proved that the empirical spectral distribution…
We consider large random matrices $X$ with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical…
Given an ensemble of NxN random matrices, a natural question to ask is whether or not the empirical spectral measures of typical matrices converge to a limiting spectral measure as N --> oo. While this has been proved for many thin…
While the wireless word moves towards higher frequency bands, new challenges arises, due to the inherent characteristics of the transmission links, such as high path and penetration losses. Penetration losses causes blockages that in turn…
We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular,…
This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…
Despite considerable work on the energy-level and wavefunction statistics of disordered quantum systems, numerical studies of those statistics relevant for electron-electron interactions in mesoscopic systems have been lacking. We plug this…
In this paper, we analyze the limiting spectral distribution of the adjacency matrix of a random graph ensemble, proposed by Chung and Lu, in which a given expected degree sequence $\overline{w}_n^{^{T}} = (w^{(n)}_1,\ldots,w^{(n)}_n)$ is…
In statistics, assuming samples are independent is reasonable. However, this property can fail to hold for the features, a distinction that has led to several lines of work aiming to remove the latter assumption of independence present in…
We study the probability distribution of the ratio of consecutive level spacings for embedded one plus two-body random matrix ensembles with and without spin degree of freedom and for both fermion and boson systems. The agreement between…
Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a…
Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the…
We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…
Based on experimental data on the newly synthesized iron-based superconductors and the relevant band structure calculations, we propose a minimal two-band BCS-type Hamiltonian with the interband Hubbard interaction included. We illustrate…
We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor…
We consider $n\times n$ real symmetric and hermitian random matrices $H_{n,m}$ equals the sum of a non-random matrix $H_{n}^{(0)}$ matrix and the sum of $m$ rank-one matrices determined by $m$ i.i.d. isotropic random vectors with…