Related papers: Distribution of lowest eigenvalue in $k$-body boso…
We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by…
The local spectral statistics of random matrices forms distinct universality classes, strongly depending on the position in the spectrum. Surprisingly, the spacing between consecutive eigenvalues at the spectral edges has received little…
It is shown that the distribution of the lowest energy eigenvalue of the quantum completions of Jackiw-Teitelboim gravity is completely described by a non-linear ordinary differential equation (ODE) arising from a non-perturbative treatment…
In this paper, we study the distribution of the minimal distance (in the Hamming metric) of a random linear code of dimension $k$ in $\mathbb{F}_q^n$. We provide quantitative estimates showing that the distribution function of the minimal…
In the past 20 years, the study of real eigenvalues of non-symmetric real random matrices has seen important progress. Notwithstanding, central questions still remain open, such as the characterization of their asymptotic statistics and the…
We propose an algorithm based on modulable hidden variables and adaptive step lengths, inspired by heuristic statistical physics and the replica method, to study the effect of mutual correlations and the emergent Wigner-Dyson distribution…
We study the statistical properties of energy spectra of two-dimensional quasiperiodic tight-binding models. We demonstrate that the nearest-neighbor level spacing distributions of these non-random systems are well described by random…
This paper proposes a new family of lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in…
We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the…
Finite sample properties of random covariance-type matrices have been the subject of much research. In this paper we focus on the "lower tail" of such a matrix, and prove that it is subgaussian under a simple fourth moment assumption on the…
Consider a high-dimensional Wishart matrix $\bd{W}=\bd{X}^T\bd{X}$ where the entries of $\bd{X}$ are i.i.d. random variables with mean zero, variance one, and a finite fourth moment $\eta$. Motivated by problems in signal processing and…
We derive an expression for the nearest-neighbor spacing distribution $P(s)$ of the energy levels of quantum systems with intermediate dynamics between regularity and chaos and missing levels due to random experimental errors. The…
We consider an $n\times n$ matrix of independent real Gaussian random variables and determine the asymptotic distribution of the smallest gaps between complex eigenvalues.
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…
We show that the limiting minimal eigenvalue distributions for a natural generalization of Gaussian sample-covariance structures (the "beta ensembles") are described by the spectrum of a random diffusion generator. By a Riccati…
We analyze eigenvalues fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that nearest neighbor spacing distribution of…
We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdos-Renyi (E-R) random graph is determined by the average degree <k>, and p(s) undergoes a…
We introduce in this paper embedded Gaussian unitary ensemble of random matrices, for $m$ fermions in $\Omega$ number of single particle orbits, generated by random two-body interactions that are SU(4) scalar, called EGUE(2)-SU(4). Here the…
Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…
We numerically study the level statistics of the Gaussian $\beta$ ensemble. These statistics generalize Wigner-Dyson level statistics from the discrete set of Dyson indices $\beta = 1,2,4$ to the continuous range $0 < \beta < \infty$. The…