Related papers: Outliers for deformed inhomogeneous random matrice…
Sharp conditions for the presence of spectral outliers are well understood for Wigner random matrices with iid entries. In the setting of inhomogeneous symmetric random matrices (i.e., matrices with a non-trivial variance profile), the…
In this work we consider general non-Hermitian square random matrices $X$ that include a wide class of random band matrices with independent entries. Whereas the existence of limiting density is largely unknown for these inhomogeneous…
Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical…
The spiked Wigner ensemble is a prototypical model for high-dimensional inference. We study the spectral properties of an inhomogeneous rank-one spiked Wigner model in which the variance of each entry of the noise matrix is itself a random…
In this paper, we study the asymptotic behavior of the outliers of the sum a Hermitian random matrix and a finite rank matrix which is not necessarily Hermitian. We observe several possible convergence rates and outliers locating around…
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 investigate the asymptotic behavior of the eigenvalues of the sum A+U*BU, where A and B are deterministic N by N Hermitian matrices having respective limiting compactly supported distributions \mu, \nu, and U is a random N by N unitary…
In this paper we characterize the possible outliers in the spectrum of large deformed unitarily invariant additive and multiplicative models, as well as the eigenvectors corresponding to them. We allow both the non-deformed unitarily…
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…
We develop a unified approach to bounding the largest and smallest singular values of an inhomogeneous random rectangular matrix, based on the non-backtracking operator and the Ihara-Bass formula for general random Hermitian matrices with a…
We study the asymptotic behavior of outliers in the spectrum of bounded rank perturbations of large random matrices. In particular, we consider perturbations of elliptic random matrices which generalize both Wigner random matrices and…
It is known that if one perturbs a large iid random matrix by a bounded rank error, then the majority of the eigenvalues will remain distributed according to the circular law. However, the bounded rank perturbation may also create one or…
For any family of $N\times N$ random matrices $(\mathbf{A}_k)_{k\in K}$ which is invariant, in law, under unitary conjugation, we give general sufficient conditions for central limit theorems for random variables of the type…
We consider symmetric and Hermitian random matrices whose entries are independent and symmetric random variables with an arbitrary variance pattern. Under a novel Short-to-Long Mixing condition, which is sharp in the sense that it precludes…
We study the eigenvalue distribution of a GUE matrix with a variance profile that is perturbed by an additive random matrix that may possess spikes. Our approach is guided by Voiculescu's notion of freeness with amalgamation over the…
The eigenvalues and eigenvectors of nonnormal matrices can be unstable under perturbations of their entries. This renders an obstacle to the analysis of numerical algorithms for non-Hermitian eigenvalue problems. A recent technique to…
Consider a random symmetric matrix with i.i.d.~entries on and above its diagonal that are products of Bernoulli random variables and random variables with sub-Gaussian tails. Such a matrix will be called a sparse Wigner matrix and can be…
We consider large-dimensional Hermitian or symmetric random matrices of the form $W=M+\vartheta V$ where $M$ is a Wigner matrix and $V$ is a real diagonal matrix whose entries are independent of $M$. For a large class of diagonal matrices…
In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues $\widehat{\lambda}_i$ and the generalized…
We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of…