Related papers: Closest Spacing of Eigenvalues

We consider $N\times N$ Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. We study the connection between eigenvalue statistics on…

We present numerical investigations demonstrating the result that the distribution of the lowest eigenvalue of finite many-boson systems (say we have $m$ number of bosons) with $k$-body interactions, modeled by Bosonic Embedded Gaussian…

In this paper, we show that the largest and smallest eigenvalues of a sample correlation matrix stemming from $n$ independent observations of a $p$-dimensional time series with iid components converge almost surely to $(1+\sqrt{\gamma})^2$…

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a…

This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example,…

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…

We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…

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…

It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…

The object of study in this paper is the expected $2$-Wasserstein distance between the empirical measures of several point processes and their respective limit. For this, the main tool developed is a smoothing procedure in Euclidean spaces…

We consider the double scaling limit in the random matrix ensemble with an external source $\frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM$ defined on $n\times n$ Hermitian matrices, where $A$ is a diagonal matrix with two eigenvalues $\pm a$ of…

We carry out a numerical study of fluctuations in the spectrum of regular graphs. Our experiments indicate that the level spacing distribution of a generic k-regular graph approaches that of the Gaussian Orthogonal Ensemble of random matrix…

Assume a finite set of complex random variables form a determinantal point process, we obtain a theorem on the limit of the empirical distribution of these random variables. The result is applied to %We study the limits of the empirical…

We show that the limiting eigenvalue density of the product of n identically distributed random matrices from an isotropic unitary ensemble (IUE) is equal to the eigenvalue density of n-th power of a single matrix from this ensemble, in the…

We study $n\times n$ random Hermitian matrix ensembles that are invariant under unitary conjugation. Let $I$ be a finite union of intervals lying in the bulk, and let $m_{k}^{(n)}$ be the $k$-th largest gap between consecutive eigenvalues…

In [earlier work by the author], it was shown that if U is a random n x n unitary matrix, then for any p>=n, the eigenvalues of U^p are i.i.d. uniform; similar results were also shown for general compact Lie groups. We study what happens…

We study the probability that all the eigenvalues of $n\times n$ Hermitian matrices, from the Laguerre unitary ensemble with the weight $x^{\gamma}\mathrm{e}^{-4nx},\;x\in[0,\infty),\;\gamma>-1$, lie in the interval $[0,\alpha]$. By using…

We present a generalization of the method of the local relaxation flow to establish the universality of local spectral statistics of a broad class of large random matrices. We show that the local distribution of the eigenvalues coincides…

Let $A$ be a $n \times n$ symmetric matrix with $(A_{i,j})_{i\leq j} $, independent and identically distributed according to a subgaussian distribution. We show that $$\mathbb{P}(\sigma_{\min}(A) \leq \varepsilon/\sqrt{n}) \leq C…

We prove an optimal estimate on the smallest singular value of a random subgaussian matrix, valid for all fixed dimensions. For an N by n matrix A with independent and identically distributed subgaussian entries, the smallest singular value…