Related papers: A note on outlier eigenvectors for sparse non-Herm…

We consider a square random matrix of size N of the form A + Y where A is deterministic and Y has iid entries with variance 1/N. Under mild assumptions, as N grows, the empirical distribution of the eigenvalues of A+Y converges weakly to a…

Consider the matrix $\Sigma_n = n^{-1/2} X_n D_n^{1/2} + P_n$ where the matrix $X_n \in \C^{N\times n}$ has Gaussian standard independent elements, $D_n$ is a deterministic diagonal nonnegative matrix, and $P_n$ is a deterministic matrix…

We study finite-rank normal deformations of rotationally invariant non-Hermitian random matrices. Extending the classical Baik-Ben Arous-P\'ech\'e (BBP) framework, we characterize the emergence and fluctuations of outlier eigenvalues in…

We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…

Let $A_n$ be an $n \times n$ deterministic matrix and $\Sigma_n$ be a deterministic non-negative matrix such that $A_n$ and $\Sigma_n$ converge in $*$-moments to operators $a$ and $\Sigma$ respectively in some $W^*$-probability space. We…

We consider large non-Hermitian $N\times N$ matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noise of variance $1/N$ completely thermalises the bulk…

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…

A large i.i.d. random matrix with deterministic low-rank perturbation has been extensively studied, particularly in the aspects of the ESD (Empirical Spectral Distribution) and the outliers of eigenvalues. In this work, we investigate the…

In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix of large size perturbed by a random matrix with small operator norm whose entries in the…

We study the eigenvalue trajectories of a time dependent matrix $ G_t = H+i t vv^*$ for $t \geq 0$, where $H$ is an $N \times N$ Hermitian random matrix and $v$ is a unit vector. In particular, we establish that with high probability, an…

We investigate the asymptotic behavior of the eigenvalues of spiked perturbations of Wigner matrices when the dimension goes to infinity. The entries of the Hermitian Wigner matrix have a distribution which is symmetric and satisfies a…

We consider a diffusive matrix process $(X_t)_{t\ge 0}$ defined as $X_t:=A+H_t$ where $A$ is a given deterministic Hermitian matrix and $(H_t)_{t\ge 0}$ is a Hermitian Brownian motion. The matrix $A$ is the "external source" that one would…

We investigate the overlap matrix between the eigenvectors of a Wigner matrix $H_{N+K}$ of size $(N+K)\times(N+K)$ and those of its principal minor $H_N$ of size $N\times N$, for both the real symmetric ($\beta=1$) and complex Hermitian…

In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block…

This paper studies inference in linear models with a high-dimensional parameter matrix that can be well-approximated by a ``spiked low-rank matrix.'' A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero…

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…

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices. We assume that the matrix entries have finite fourth moment and extend the results by Capitaine, Donati-Martin, and F\'eral for…

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…

Using large $N$ arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large $N$ limit. The setting generalizes the quaternionic extension of free probability to…

We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices. Specifically, we prove almost sure convergence of the extreme eigenvalues and appropriate projections of the corresponding eigenvectors of…