相关论文: Asymptotics of random density matrices

Let A be a p-variate real Wishart matrix on n degrees of freedom with identity covariance. The distribution of the largest eigenvalue in A has important applications in multivariate statistics. Consider the asymptotics when p grows in…

We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…

The correlated Wishart model provides the standard benchmark when analyzing time series of any kind. Unfortunately, the real case, which is the most relevant one in applications, poses serious challenges for analytical calculations. Often…

We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by…

This paper is the second chapter of three of the author's undergraduate thesis. In this paper, we consider the random matrix ensemble given by $(d_b, d_w)$-regular graphs on $M$ black vertices and $N$ white vertices, where $d_b \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 apply the method of determinants to study the distribution of the largest singular values of large $ m \times n $ real rectangular random matrices with independent Cauchy entries. We show that statistical properties of the (rescaled by a…

We study the joint probability density of the eigenvalues of a product of rectangular real, complex or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only…

Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…

In this paper we construct a class of random matrix ensembles labelled by a real parameter $\alpha \in (0,1)$, whose eigenvalue density near zero behaves like $|x|^\alpha$. The eigenvalue spacing near zero scales like $1/N^{1/(1+\alpha)}$…

We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful…

We prove nonasymptotic matrix concentration inequalities for the spectral norm of (sub)gaussian random matrices with centered independent entries that capture fluctuations at the Tracy-Widom scale. This considerably improves previous bounds…

In recent years the Rosenzweig--Porter (RP) ensemble, obtained by adding a diagonal matrix with independent and identically distributed elements to a Gaussian random matrix, has been widely used as a minimal model for the emergence of…

Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…

We studied the universality of Wishart ensembles whose covariance matrix has 2 distinct eigenvalues. We studied the asymptotic limit when the number of both eigenvalues goes to infinity and obtained universality results. In this case, the…

Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…

We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of…

We investigate $\beta$-Generalized random Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We investigate general method names as equilibrium…