Related papers: On the Central Limit Theorem for linear eigenvalue…
We study the point process $W$ in $\mathbb{R}^d$ obtained by adding an independent Gaussian vector to each point in $\mathbb{Z}^d$. Our main concern is the asymptotic size of fluctuations of the linear statistics in the large volume limit,…
Enriquez, Faraud, and Lemaire (2023) have established process-level fluctuations for the giant of the dynamic Erd\H{o}s-R\'{e}nyi random graph above criticality and show that the limit is a centered Gaussian process with continuous sample…
This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
The power spectrum of weak lensing fluctuations has a non-Gaussian distribution due to its quadratic nature. On small scales the Central Limit Theorem acts to Gaussianize this distribution but non-Gaussianity in the signal due to…
The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a…
We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a gaussian random variable. We find an…
We obtain bounds on the distribution of normalized gaps of eigenvalues of $N \times N$ GUE matrix in the bulk, that do not lose logarithmic factors of $N$ in the limit $N \to \infty$. As an application, we obtain fixed index universality…
This work addresses the Galerkin isogeometric discretization of the one-dimensional Laplace eigenvalue problem subject to homogeneous Dirichlet boundary conditions on a bounded interval. We employ GLT theory to analyze the behavior of the…
An appropriate model for the random energy landscape in organic glasses is a spatially correlated Gaussian field. We calculated the distribution of the average value of a Gaussian random field in a finite domain. The results of the…
We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically.…
Linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems. The proofs of such results are usually rather difficult, involving hard computations specific to the model in…
A generalized Wigner matrix perturbed by a finite-rank deterministic matrix is considered. The fluctuations of the largest eigenvalues, which emerge outside the bulk of the spectrum, and the corresponding eigenvectors, are studied. Under…
We present a quantum ergodicity theorem for fixed spectral window and sequences of compact hyperbolic surfaces converging to the hyperbolic plane in the sense of Benjamini and Schramm. This addresses a question posed by Colin de…
We study sample-to-sample fluctuations in a critical two-dimensional Ising model with quenched random ferromagnetic couplings. Using replica calculations in the renormalization group framework we derive explicit expressions for the…
We study the distribution of the largest eigenvalue in the "Pfaffian" classical ensembles of random matrix theory, namely in the Gaussian orthogonal (GOE) and Gaussian symplectic (GSE) ensembles, using semi-classical skew-orthogonal…
The degree of entanglement of random pure states in bipartite quantum systems can be estimated from the distribution of the extreme Schmidt eigenvalues. For a bipartition of size M\geq N, these are distributed according to a…
We study two closely related problems stemming from the random wave conjecture for Maass forms. The first problem is bounding the $L^4$-norm of a Maass form in the large eigenvalue limit; we complete the work of Spinu to show that the…
The focus of this paper is on the probability, $E_\beta(0;J)$, that a set $J$ consisting of a finite union of intervals contains no eigenvalues for the finite $N$ Gaussian Orthogonal ($\beta=1$) and Gaussian Symplectic ($\beta=4$) Ensembles…
We study the variance in the number of points contained within a window $\Omega$ of arbitrary size, and to further illuminate our understanding of {\it hyperuniform} systems, i.e., point patterns that do not possess long-wavelength…