Related papers: Characteristic polynomials for random band matrice…
We show Poisson statistics for random band matrices which diagonal entries have Gaussian components. These components are possibly as small as $n^{-\varepsilon}$. Particularly, our result is applicable for a band matrix cut from the GUE…
In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…
This paper can be thought of as a remark of \cite{llw}, where the authors studied the eigenvalue distribution $\mu_{X_N}$ of random block Toeplitz band matrices with given block order $m$. In this note we will give explicit density…
We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small off-diagonal elements…
We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
This paper is concerned with the statistical properties of the Gram matrix $\mathbf{W}=\mathbf{H}\mathbf{H}^\dagger$, where $\mathbf{H}$ is a $2\times2$ complex central Gaussian matrix whose elements have arbitrary variances. With such…
We study the eigenvalue correlations of random Hermitian $n\times n$ matrices of the form $S=M+\epsilon H$, where $H$ is a GUE matrix, $\epsilon>0$, and $M$ is a positive-definite Hermitian random matrix, independent of $H$, whose…
We study the averaged product of characteristic polynomials of large random matrices in the Gaussian beta-ensemble perturbed by an external source of finite rank. We prove that at the edge of the spectrum, the limiting correlations involve…
We propose a new definition of characteristic polynomials of tensors based on a partition function of Grassmann variables. This new notion of characteristic polynomial addresses general tensors including totally antisymmetric ones, but not…
We describe the spectral statistics of the first finite number of eigenvalues in a newly-forming band on the hard-edge of the spectrum of a random Hermitean matrix model. It is found that in a suitable scaling regime, they are described by…
We consider a random matrix whose entries are independent Gaussian variables taking values in the field of quaternions with variance $1/n$. Using logarithmic potential theory, we prove the almost sure convergence, as the dimension $n$ goes…
We study correlation functions of the characteristic polynomials in coupled matrix models based on the Schur polynomial expansion, which manifests their determinantal structure.
An expansion of the Weyl function of a $H$-selfadjoint random matrix with one negative square is provided. It is shown that the coefficients converge to a certain generalization of Catlan numbers. Properties of this generalization are…
We study some mesoscopic properties of electron transport by employing one-dimensional chains and Anderson tight-binding model. Principal attention is paid to the resistance of finite-length chains with disordered white-noise potential. We…
We consider $N\times N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semi-circle form over $[-\sqrt{2},\sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the…
We study certain probability measures on partitions of n=1,2,..., originated in representation theory, and demonstrate their connections with random matrix theory and multivariate hypergeometric functions. Our measures depend on three…
We investigate concentration properties of spectral measures of Hermitian random matrices with partially dependent entries. More precisely, let $X_n$ be a Hermitian random matrix of size $n\times n$ that can be split into independent blocks…
We show the eigenvectors of a Gaussian random band matrix are localized when the band width is less than the 1/4 power of the matrix size. Our argument is essentially an optimized version of Schenker's proof of the 1/8 exponent.
We study sample covariance matrices arising from multi-level components of variance. Thus, let $ B_n=\frac{1}{N}\sum_{j=1}^NT_{j}^{1/2}x_jx_j^TT_{j}^{1/2}$, where $x_j\in R^n$ are i.i.d. standard Gaussian, and…