Related papers: Eigenvalue distribution of nonlinear models of ran…

In this paper, we analyze the limiting spectral distribution of the adjacency matrix of a random graph ensemble, proposed by Chung and Lu, in which a given expected degree sequence $\overline{w}_n^{^{T}} = (w^{(n)}_1,\ldots,w^{(n)}_n)$ is…

We study the eigenvalues and the eigenvectors of $N\times N$ structured random matrices of the form $H = W\tilde{H}W+D$ with diagonal matrices $D$ and $W$ and $\tilde{H}$ from the Gaussian Unitary Ensemble. Using the supersymmetry technique…

We consider a versatile matrix model of the form ${\bf A}+i {\bf B}$, where ${\bf A}$ and ${\bf B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive…

We analyze gene co-expression network under the random matrix theory framework. The nearest neighbor spacing distribution of the adjacency matrix of this network follows Gaussian orthogonal statistics of random matrix theory (RMT). Spectral…

The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential…

We consider the empirical eigenvalue distribution of an $m\times m$ principal submatrix of an $n\times n$ random unitary matrix distributed according to Haar measure. For $n$ and $m$ large with $\frac{m}{n}=\alpha$, the empirical spectral…

In this paper we consider Wigner random matrices -- symmetric n by n random matrices whose entries are independent identically distributed real random variables. We prove that the probability distribution of one or several eigenvalues close…

The paper studies the problem of distributed parameter estimation in multi-agent networks with exponential family observation statistics. A certainty-equivalence type distributed estimator of the consensus + innovations form is proposed in…

The ability to estimate joint, conditional and marginal probability distributions over some set of variables is of great utility for many common machine learning tasks. However, estimating these distributions can be challenging,…

We give a short, operator-theoretic proof of the asymptotic independence (including a first correction term) of the minimal and maximal eigenvalue of the n \times n Gaussian Unitary Ensemble in the large matrix limit n \to \infty. This is…

In random matrix theory, Marchenko-Pastur law states that random matrices with independent and identically distributed entries have a universal asymptotic eigenvalue distribution under large dimension limit, regardless of the choice of…

This technical report describes the derivation of the asymptotic eigenvalue distribution for causal 2D-AR models under an upscaling scenario. Specifically, it tackles the analytical derivation of the asymptotic eigenvalue distribution of…

In deriving large n probability distribution function of the rightmost eigenvalue from the classical Random Matrix Theory Ensembles, one is faced with que question of finding large n asymptotic of certain coupled set of functions. This…

In this paper, we consider a data matrix $X_N\in\mathbb{R}^{N\times p}$ where all the rows are i.i.d. samples in $\mathbb{R}^p$ of mean zero and covariance matrix $\Sigma\in\mathbb{R}^{p\times p}$. Here the population matrix $\Sigma$ is of…

We consider a class of sparse random matrices, which includes the adjacency matrix of Erd\H{o}s-R\'enyi graph ${\bf G}(N,p)$. For $N^{-1+o(1)}\leq p\leq 1/2$, we show that the non-trivial edge eigenvectors are asymptotically jointly normal.…

Let g:{\mathbb R} --> {\mathbb C} be a C^{\infty}-function with all derivatives bounded and let tr_n denote the normalized trace on the n x n matrices. In the paper [EM] Ercolani and McLaughlin established asymptotic expansions of the mean…

Symplectic ensemble of disordered non-Hermitian Hamiltonians is studied. Starting from a model with an imaginary magnetic field, we derive a proper supermatrix $\sigma $-model. The zero-dimensional version of this model corresponds to a…

Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…

Consider a random matrix whose variance profile is random. This random matrix is ergodic in one channel realization if, for each column and row, the empirical distribution of the squared magnitudes of elements therein converges to a…

In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…