Related papers: Fluctuations of random matrix products and 1D Dira…

Consider Ginibre's ensemble of $N \times N$ non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance $\frac{1}{N}$. As $N \uparrow \infty$ the normalized counting measure of the…

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…

Consider the random variable $\mathrm{Tr}( f_1(W)A_1\dots f_k(W)A_k)$ where $W$ is an $N\times N$ Hermitian Wigner matrix, $k\in\mathbb{N}$, and choose (possibly $N$-dependent) regular functions $f_1,\dots, f_k$ as well as bounded…

We study products of arbitrary random real $2 \times 2$ matrices that are close to the identity matrix. Using the Iwasawa decomposition of $\text{SL}(2,{\mathbb R})$, we identify a continuum regime where the mean values and the covariances…

Let $M_n$ be a $n \times n$ Wigner or sample covariance random matrix, and let $\mu_1(M_n), \mu_2(M_n), ..., \mu_n(M_n)$ denote the unordered eigenvalues of $M_n$. We study the fluctuations of the partial linear eigenvalue statistics $$…

We perform an analysis of preliminary data on strange particles yields and fluctuations within the Statistical hadronization model. We begin by describing the theoretical disagreements between different statistical models currently on the…

We study fluctuation properties of embedded random matrix ensembles of non-interacting particles. For ensemble of two non-interacting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are…

Consider the product $X = X_{1}\cdots X_{m}$ of $m$ independent $n\times n$ iid random matrices. When $m$ is fixed and the dimension $n$ tends to infinity, we prove Gaussian limits for the centered linear spectral statistics of $X$ for…

We prove that the Lyapunov exponents of random products in a (real or complex) matrix group depends continuously on the matrix coefficients and probability weights. More generally, the Lyapunov exponents of the random product defined by any…

Dirac fermions on a two-dimensional lattice with disorder are considered. The Dirac mass, which controls the gap between the two bands of the fermions, is subject to random fluctuations. Another type of disorder is discussed presented by a…

We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we…

We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A.Lytova…

Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder these systems can…

We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of $M$ independent iid random matrices, as $M$ is fixed, and the sizes of the matrices tend to infinity. This…

We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an $n \times n$ matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian…

For each $n$, let $A_n=(\sigma_{ij})$ be an $n\times n$ deterministic matrix and let $X_n=(X_{ij})$ be an $n\times n$ random matrix with i.i.d. centered entries of unit variance. In the companion article Cook et al., we considered the…

Random-matrix theory is used to study the mesoscopic fluctuations of the excitation gap in a metal grain or quantum dot induced by the proximity to a superconductor. We propose that the probability distribution of the gap is a universal…

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…

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic $\sum_{j=1}^N (x_j - <x>)$ is computed exactly and shown to satisfy a central limit theorem as $N \to \infty$. For the…

In this paper, we consider $m$ independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables and assume the product of the $m$ rectangular matrices is an $n$ by…