相关论文: Large Deviations of the Maximum Eigenvalue in Wish…

In this paper, we study the fluctuation of linear eigenvalue statistics of Random Band Matrices defined by $M_{n}=\frac{1}{\sqrt{b_{n}}}W_{n}$, where $W_{n}$ is a $n\times n$ band Hermitian random matrix of bandwidth $b_{n}$, i.e., the…

The statistics of the smallest eigenvalue of Wishart-Laguerre ensemble is important from several perspectives. The smallest eigenvalue density is typically expressible in terms of determinants or Pfaffians. These results are of utmost…

Wishart random matrices are often used to model multivariate systems in physics, finance, biology and wireless communication. Extreme value statistics, such as those of the smallest eigenvalue, can be used to test the accuracy of the model.…

Consider a deterministic self-adjoint matrix X_n with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by…

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…

Let $X^{(\delta)}$ be a Wishart process of dimension $\delta$, with values in the set of positive matrices of size $m$. We are interested in the large deviations for a family of matrix-valued processes $\{\delta^{-1} X_t^{(\delta)}, t \leq…

We investigate the fluctuations of linear spectral statistics of a Wigner matrix $W\_N$ deformed by a deterministic diagonal perturbation $D\_N$, around a deterministic equivalent which can be expressed in terms of the free convolution…

We compute exact asymptotic of the statistical density of random matrices belonging to the Generalized Gaussian orthogonal, unitary and symplectic ensembles such that there no eigenvalues in the interval $[\sigma, +\infty[$. In particular,…

Rectangular real $N \times (N + \nu)$ matrices $W$ with a Gaussian distribution appear very frequently in data analysis, condensed matter physics and quantum field theory. A central question concerns the correlations encoded in the spectral…

Let $\mathbf{W}\in\mathbb{C}^{n\times n}$ be a {\it single-spiked} Wishart matrix in the class $\mathbf{W}\sim \mathcal{CW}_n(m,\mathbf{I}_n+ \theta \mathbf{v}\mathbf{v}^\dagger) $ with $m\geq n$, where $\mathbf{I}_n$ is the $n\times n$…

This short note studies the fluctuations of the largest eigenvalue of symmetric random matrices with correlated Gaussian entries having positive mean. Under the assumption that the covariance kernel is absolutely summable, it is proved that…

We consider random matrices of the form $H = W + \lambda V$, $\lambda\in\mathbb{R}^+$, where $W$ is a real symmetric or complex Hermitian Wigner matrix of size $N$ and $V$ is a real bounded diagonal random matrix of size $N$ with i.i.d.\…

We consider the Laguerre Unitary Ensemble (aka, Wishart Ensemble) of sample covariance matrices $A = XX^*$, where $X$ is an $N \times n$ matrix with iid standard complex normal entries. Under the scaling $n = N + \lfloor \sqrt{ 4 c N}…

We prove that the number of iterations required to solve a random positive definite linear system with the conjugate gradient algorithm is almost deterministic for large matrices. We treat the case of Wishart matrices $W = XX^*$ where $X$…

We establish a quantitative version of the Tracy--Widom law for the largest eigenvalue of high dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix…

Eigenvalues of Wigner matrices has been a major topic of investigation. A particularly important subclass of such random matrices is formed by the adjacency matrix of an Erd\H{o}s-R\'{e}nyi graph $\mathcal{G}_{n,p}$ equipped with i.i.d.…

In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…

It has been recently shown that if $X$ is an $n\times N$ matrix whose entries are i.i.d. standard complex Gaussian and $l_1$ is the largest eigenvalue of $X^*X$, there exist sequences $m_{n,N}$ and $s_{n,N}$ such that…

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4)…

The eigenvalue statistics for complex $N \times N$ Wishart matrices $X_{r,s}^\dagger X_{r,s}$, where $ X_{r,s}$ is equal to the product of $r$ complex Gaussian matrices, and the inverse of $s$ complex Gaussian matrices, are considered. In…