Related papers: Outlier eigenvalues for full rank deformed single …

In this paper, we consider a sequence of selfadjoint matrices $A_n$ having a limiting spectral distribution as $n\to \infty$, and we consider a sequence of full flags $\{0\le p_1^n\le\ldots\le p_i^n\le\ldots\le 1_n\}$ chosen at random…

Consider the random bipartite Erd\H{o}s-R\'{e}nyi graph $\mathbb{G}(n, m, p)$, where each edge with one vertex in $V_{1}=[n]$ and the other vertex in $V_{2} =[m]$ is connected with probability $p$, and $n=\lfloor \gamma m\rfloor$ for a…

This paper is to investigate the spectral properties of sample covariance matrices under a more general population. We consider a class of matrices of the form $\mathbf S_n=\frac1n\mathbf B_n\mathbf X_n\mathbf X_n^*\mathbf B_n^*$, where…

In this paper, we study the effect of sparsity on the appearance of outliers in the semi-circular law. Let $(W_n)_{n=1}^\infty$ be a sequence of random symmetric matrices such that each $W_n$ is $n\times n$ with i.i.d entries above and on…

We consider the deformed Laguerre Ensemble $H_n=\dfrac{1}{m}\Sigma_n^{1/2}A_{m,n}A_{m,n}^*\Sigma_n^{1/2}$ in which $\Sigma_n$ is a positive hermitian matrix (possibly random) and $A_{m,n}$ is a $n\times m$ complex Gaussian random matrix…

Consider the $n\times n$ matrix $X_n=A_n+H_n$, where $A_n$ is a $n\times n$ matrix (either deterministic or random) and $H_n$ is a $n\times n$ matrix independent from $A_n$ drawn from complex Ginibre ensemble. We study the limiting…

Fix positive numbers $\alpha$ and $\beta$. For the family of doubly cyclic matrices of the form $diag(a_1, a_2, ... ,a_n) - diag(b_1, b_2, ... ,b_n) \Sigma_*$, where $\Sigma_*$ is a permutation matrix for the $n$-cycle $1 \to 2$, $2 \to 3$,…

Improving upon results of Rudelson and Vershynin, we establish delocalization bounds for eigenvectors of independent-entry random matrices. In particular, we show that with high probability every eigenvector is delocalized, meaning any…

Let $A$ be a square random matrix of size $n$, with mean zero, independent but not identically distributed entries, with variance profile $S$. When entries are i.i.d. with unit variance, the spectral radius of $n^{-1/2}A$ converges to $1$…

Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the…

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

Consider a random matrix of size $N$ as an additive deformation of the complex Ginibre ensemble under a deterministic matrix $X_0$ with a finite rank, independent of $N$. When some eigenvalues of $X_0$ separate from the unit disk, outlier…

For a division ring $D$, denote by $\mathcal M_D$ the $D$-ring obtained as the completion of the direct limit $\varinjlim_n M_{2^n}(D)$ with respect to the metric induced by its unique rank function. We prove that, for any ultramatricial…

Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…

Random Hermitian matrices with a source term arise, for instance, in the study of non-intersecting Brownian walkers \cite{Adler:2009a, Daems:2007} and sample covariance matrices \cite{Baik:2005}. We consider the case when the $n\times n$…

We study the geometry of the first two eigenvalues of a magnetic Steklov problem on an annulus $\Sigma$ (a compact Riemannian surface with genus zero and two boundary components), the magnetic potential being the harmonic one-form having…

Inhomogeneous random matrices with non-trivial variance profiles determined by symmetric stochastic matrices and with independent sub-Gaussian entries up to Hermitian symmetry, encompass a wide range of important models, including sparse…

Using the results on the $1/n$-expansion of the Verblunsky coefficients for a class of polynomials orthogonal on the unit circle with $n$ varying weight, we prove that the local eigenvalue statistic for unitary matrix models is independent…

Let $\Omega\subset \mathbb R^2$ be a bounded planar domain, with piecewise smooth boundary $\partial \Omega$. For $\sigma>0$, we consider the Robin boundary value problem \[ -\Delta f =\lambda f, \qquad \frac{\partial f}{\partial n} +…

Given a selfadjoint polynomial $P(X,Y)$ in two noncommuting selfadjoint indeterminates, we investigate the asymptotic eigenvalue behavior of the random matrix $P(A\_N,B\_N)$, where $A\_N$ and $B\_N$ are independent Hermitian random matrices…