相关论文: Two-band random matrices

Random matrix theory, which characterizes spectral distributions of infinitely large matrices, plays a central role across diverse fields, including high-dimensional data analysis, ecology, neuroscience, and machine learning. Among its key…

We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…

Correspondence in quantum chaotic systems is lost in short time scales. Introducing some noise we study the spectrum of the resulting coarse grained propagaor of density matrices. Some differen methods to compute the spectrum are reviewed.…

We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…

The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…

We consider inhomogeneous square random matrices of size $N$ with independent entries of mean 0 and finite variance. We assume that the variance profile of this matrix is doubly stochastic and has a band-like structure with an appropriately…

We study the overlaps between eigenvectors of nonnormal matrices. They quantify the stability of the spectrum, and characterize the joint eigenvalues increments under Dyson-type dynamics. Well known work by Chalker and Mehlig calculated the…

We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the…

We obtain uniform asymptotics for polynomials orthogonal on a fixed and varying arc of the unit circle with a positive analytic weight function. We also complete the proof of the large $s$ asymptotic expansion for the Fredholm determinant…

We study concentration in spectral norm of nonparametric estimates of correlation matrices. We work within the confine of a Gaussian copula model. Two nonparametric estimators of the correlation matrix, the sine transformations of the…

This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. We show that the…

We show that in the large matrix limit, the eigenvalues of the normal matrix model for matrices with spectrum inside a compact domain with a special class of potentials homogeneously fill the interior of a polynomial curve uniquely defined…

We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…

This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral…

We analyze the spectral properties of the high-dimensional random geometric graph $G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever…

Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and…

We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the…

This paper investigates limiting spectral distribution of a high-dimensional Kendall's rank correlation matrix. The underlying population is allowed to have general dependence structure. The result no longer follows the generalized…

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 introduce a family of coefficients based on U-statistics that generalize the notion of correlation and explore their properties in the large dimensional multivariate case, showing that in the null case of uncorrelated variables, the…