Related papers: Universality in the two matrix model: a Riemann-Hi…

We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…

We study the behavior of eigenvalues of matrix P_N + Q_N where P_N and Q_N are two N -by-N random orthogonal projections. We relate the joint eigenvalue distribution of this matrix to the Jacobi matrix ensemble and establish the universal…

We obtain the explicit rate of convergence $N^{-1/2 + \epsilon}$ for the gaps of generalized Wigner matrices in the bulk of the spectrum, for distributions of matrix entries possibly atomic and supported on enough points. The proof proceeds…

In this paper, we investigate the asymptotic spectrum of complex or real Deformed Wigner matrices $(M_N)_N$ defined by $M_N=W_N/\sqrt{N}+A_N$ where $W_N$ is an $N\times N$ Hermitian (resp., symmetric) Wigner matrix whose entries have a…

The recursively-constructed family of Mandelbrot matrices $M_n$ for $n=1$, $2$, $\ldots$ have nonnegative entries (indeed just $0$ and $1$, so each $M_n$ can be called a binary matrix) and have eigenvalues whose negatives $-\lambda = c$…

Generalizations of the Hermite polynomials to many variables and/or to the complex domain have been located in mathematical and physical literature for some decades. Polynomials traditionally called complex Hermite ones are mostly…

It is a result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n\times n$ Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process…

For the unitary ensembles of $N\times N$ Hermitian matrices associated with a weight function $w$ there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For…

We consider $N\times N$ symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove…

In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues for regular quadratic eigenvalue problems of the form $\lambda^2 M x + \lambda C x + K x = 0$, where $M$ and $K$ are nonsingular Hermitian matrices…

We obtain Plancherel-Rotach type asymptotics valid in all regions of the complex plane for orthogonal polynomials with varying weights of the form $e^{-NV(x)}$ on the real line, assuming that $V$ has only two Lipschitz continuous…

We consider ensembles of random matrices, known as biorthogonal ensembles, whose eigenvalue probability density function can be written as a product of two determinants. These systems are closely related to multiple orthogonal functions. It…

Assume that the eigenvalues of a finite hermitian linear operator have been deduced accurately but the linear operator itself could not be determined with precision. Given a set of eigenvalues $\lambda$ and a hermitian matrix $M$, this…

We describe the resolvent approach for the rigorous study of the mescoscopic regime of Hermitian matrix spectra. We present results reflecting the universal behavior of the smoothed density of eigenvalue distribution of large random…

Let $\bm{x}_1,\cdots,\bm{x}_n$ be a random sample of size $n$ from a $p$-dimensional population distribution, where $p=p(n)\rightarrow\infty$. Consider a symmetric matrix $W=X^\top X$ with parameters $n$ and $p$, where…

We consider the limiting location and limiting distribution of the largest eigenvalue in real symmetric ($\beta$ = 1), Hermitian ($\beta$ = 2), and Hermitian self-dual ($\beta$ = 4) random matrix models with rank 1 external source. They are…

We consider $N\times N$ random matrices of the form $H = W + V$ where $W$ is a real symmetric Wigner matrix and $V$ a random or deterministic, real, diagonal matrix whose entries are independent of $W$. We assume subexponential decay for…

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian…

We consider an ensemble of self-dual matrices with arbitrary complex entries. This ensemble is closely related to a previously defined ensemble of anti-symmetric matrices with arbitrary complex entries. We study the two-level correlation…

We consider four nontrivial ensembles involving Gaussian Wigner and Wishart matrices. These are relevant to problems ranging from multiantenna communication to random supergravity. We derive the matrix probability density, as well as the…