相关论文: Spectral Density for Random Matrices with Independ…

We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be…

We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…

We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…

For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists…

The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…

Limiting Spectral Distributions (LSD) of real symmetric patterned matrices have been well-studied. In this article, we consider skew-symmetric/anti-symmetric patterned random matrices and establish the LSDs of several common matrices. For…

This paper studies the behaviour of the empirical eigenvalue distribution of large random matrices W_N W_N* where W_N is a ML x N matrix, whose M block lines of dimensions L x N are mutually independent Hankel matrices constructed from…

We consider the eigenvalues of sample covariance matrices of the form $\mathcal{Q}=(\Sigma^{1/2}X)(\Sigma^{1/2}X)^*$. The sample $X$ is an $M\times N$ rectangular random matrix with real independent entries and the population covariance…

We examine the empirical distribution of the eigenvalues and the eigenvectors of adjacency matrices of sparse regular random graphs. We find that when the degree sequence of the graph slowly increases to infinity with the number of…

We consider an indexed class of real symmetric random matrices which generalize the symmetric Hankel and Reverse Circulant matrices. We show that the limiting spectral distributions of these matrices exist almost surely and the limit is…

In this paper we show that the empirical eigenvalue distribution of any sample covariance matrix generated by independent copies of a stationary regular sequence has a limiting distribution depending only on the spectral density of the…

Non-Hermitian random matrices with statistical spectral characteristics beyond the standard Ginibre ensembles have recently emerged in the description of dissipative quantum many-body systems as well as in non-ergodic wave transport in…

We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found…

We compare eigenvalue densities of Wigner random matrices whose elements are independent identically distributed (iid) random numbers with a Levy distribution and maximally random matrices with a rotationally invariant measure exhibiting a…

Although the spectra of random networks have been studied for a long time, the influence of network topology on the dense limit of network spectra remains poorly understood. By considering the configuration model of networks with four…

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…

It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…

We investigate the asymptotic behavior of the eigenvalues of spiked perturbations of Wigner matrices when the dimension goes to infinity. The entries of the Hermitian Wigner matrix have a distribution which is symmetric and satisfies a…

In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest eigenvalues of the adjacency and the…

The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of…