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We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some…

We study the asymptotic spectral behavior of high-dimensional random Gram matrices with sparsity and a variance profile, motivated by applications in wireless communications. Specifically, we consider the Gram matrices $\mathbf S_n=\mathbf…

Bi-clustering is a technique that allows for the simultaneous clustering of observations and features in a dataset. This technique is often used in bioinformatics, text mining, and time series analysis. An important advantage of…

We prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. Our techniques rely on a…

We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry,…

In arXiv:1410.7268v3, the authors consider eigenvalues of overlapping Wishart matrices and prove that its fluctuations asymptotically convergence to the Gaussian free field. In this brief note, their result is extended to show that when the…

. We study the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random perturbation drawn from (i) a generalized Gaussian ensemble (ii) a non-Gaussian ensemble with a measure variable under the change of…

Scaling arguments are used to constrain the angular spectrum of distortions on boundaries of macroscopic causal diamonds, produced by Planck-scale vacuum fluctuations of causally-coherent quantum gravity. The small-angle spectrum of…

In this note, we study the Gaussian fluctuations for the Wishart matrices $d^{-1}\mathcal{X}_{n, d}\mathcal{X}^{T}_{n, d}$, where $\mathcal{X}_{n, d}$ is a $n\times d$ random matrix whose entries are jointly Gaussian and correlated with row…

In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…

We study the universality property of estimators for high-dimensional linear models, which implies that the distribution of estimators is independent of whether the covariates follow a Gaussian distribution. Recent developments in…

We proposed a new universal method for significantly increasing accuracy of critical points of 2 and 3-dimensional Ising models and exploring fluctuation mechanism. The method is based on analysis of block fractals and the renormalization…

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…

We give a two-dimensional central limit theorem (CLT) for the second-order quadratic variation of the centered Gaussian processes on $[0,T]$. Though the approach we use is well known in the literature, the conditions under which the CLT…

We study fluctuations of mean-field interacting particle systems around their McKean--Vlasov limit. Our main result provides a uniform-in-time quantitative central limit theorem for the fluctuation process, with convergence rate of order…

Let $G=G(n,p_n)$ be a homogeneous Erd\"os-R\'enyi graph, and $A$ its adjacency matrix with eigenvalues $\lambda_1(A) \geq \lambda_2(A) \geq ... \geq \lambda_n(A).$ Local laws have been used to show that $lambda_2(A)$ can exhibit…

We study the effects of an arbitrary external perturbation in the statistical properties of the S-matrix of quantum chaotic scattering systems in the limit of isolated resonances. We derive, using supersymmetry, an exact non-perturbative…

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent…

The fluctuations in the cosmic microwave background radiation may contain deviations from gaussian statistics which would be reflected in a nonzero value of three-point correlation function of $\Delta T$. However, any potential observation…

This article carries out a large dimensional analysis of standard regularized discriminant analysis classifiers designed on the assumption that data arise from a Gaussian mixture model with different means and covariances. The analysis…