相关论文: On Fluctuations of Matrix Entries of Regular Funct…
Inspired by a recent paper of I. Grama, E. Le Page and M. Peign\'e, we consider a sequence $(g_n)_{n \geq 1}$ of i.i.d. random $d\times d$-matrices with non-negative entries and study the fluctuations of the process $(\log \vert g_n\cdots…
We present the correct space of test functions for the Ornstein-Uhlenbeck processes defined in \cite{fgn2}. Under these new spaces, an invariance with respect to a second order operator is shown, granting the existence and uniqueness of…
Metaplectic Wigner distributions are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigner distribution. We investigate the question which…
It is well known that the weak limit of a suitably scaled continuous-time random walk (CTRW) is the Brownian motion. We investigate the convergence of certain patterned random matrices whose entries are independent CTRWs and their…
We consider the distribution of the top eigenvector $\widehat{v}$ of a spiked matrix model of the form $H = \theta vv^* + W$, in the supercritical regime where $H$ has an outlier eigenvalue of comparable magnitude to $\|W\|$. We show that,…
We prove the universal asymptotically almost sure non-singularity of general Ginibre and Wigner ensembles of random matrices when the distribution of the entries are independent but not necessarily identically distributed and may depend on…
We present a possible extension of the random-matrix theory, which is widely used to describe spectral fluctuations of chaotic systems. By considering the Kaniadakis non-Gaussian statistics, characterized by the index {\kappa}…
For large dimensional non-Hermitian random matrices $X$ with real or complex independent, identically distributed, centered entries, we consider the fluctuations of $f(X)$ as a matrix where $f$ is an analytic function around the spectrum of…
Consider an ensemble of $N\times N$ non-Hermitian matrices in which all entries are independent identically distributed complex random variables of mean zero and absolute mean-square one. If the entry distributions also possess bounded…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
In this paper we study ensembles of random symmetric matrices $\X_n = {X_{ij}}_{i,j = 1}^n$ with dependent entries such that $\E X_{ij} = 0$, $\E X_{ij}^2 = \sigma_{ij}^2$, where $\sigma_{ij}$ may be different numbers. Assuming that the…
For a sufficiently nice 2 dimensional shape, we define its approximating matrix (or patterned matrix) as a random matrix with iid entries arranged according to a given pattern. For large approximating matrices, we observe that the…
This is an elementary review, aimed at non-specialists, of results that have been obtained for the limiting distribution of eigenvalues and for the operator norms of real symmetric random matrices via the method of moments. This method goes…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…
The model of heavy Wigner matrices generalizes the classical ensemble of Wigner matrices: the sub-diagonal entries are independent, identically distributed along to and out of the diagonal, and the moments its entries are of order 1/N,…
Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival…
We consider the quadratic optimization problem $$F_n^{W,h}:= \sup_{x \in S^{n-1}} ( x^T W x/2 + h^T x )\,, $$ with $W$ a (random) matrix and $h$ a random external field. We study the probabilities of large deviation of $F_n^{W,h}$ for $h$ a…
In this paper, we investigate the fluctuations of a unit eigenvector associated to an outlier in the spectrum of a spiked $N\times N$ complex Deformed Wigner matrix $M_N$: $M_N =W_N/\sqrt{N} + A_N$ where $W_N$ is an $N \times N$ Hermitian…
The Wigner distribution is a milestone of Time-frequency Analysis. In order to cope with its drawbacks while preserving the desirable features that made it so popular, several kind of modifications have been proposed. This contributions…
Products of random $2\times 2$ matrices exhibit Gaussian fluctuations around almost surely convergent Lyapunov exponents. In this paper, the distribution of the random matrices is supported by a small neighborhood of order $\lambda>0$ of…