Related papers: Random Matrices with Slow Correlation Decay
The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially…
We consider a decision network on an undirected graph in which each node corresponds to a decision variable, and each node and edge of the graph is associated with a reward function whose value depends only on the variables of the…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
The celebrated elliptic law describes the distribution of eigenvalues of random matrices with correlations between off-diagonal pairs of elements, having applications to a wide range of physical and biological systems. Here, we investigate…
We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small off-diagonal elements…
We study random points on the real line generated by the eigenvalues in unitary invariant random matrix ensembles or by more general repulsive particle systems. As the number of points tends to infinity, we prove convergence of the…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
A class of discrete renewal processes with super-exponentially decaying inter-arrival distributions coincides with the infinite volume limit of general homogeneous pinning models in their localized phase. Pinning models are statistical…
We present here a general iterative formula which gives a (formal) series expansion for the time autocorrelation of smooth dynamical variables, for all Hamiltonian systems endowed with an invariant measure. We add some criteria, theoretical…
We precisely quantify the impact of statistical error in the quality of a numerical approximation to a random matrix eigendecomposition, and under mild conditions, we use this to introduce an optimal numerical tolerance for residual error…
Random matrix models consisting of normal matrices, defined by the sole constraint $[N^{\dag},N]=0$, will be explored. It is shown that cubic eigenvalue repulsion in the complex plane is universal with respect to the probability…
Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…
This paper presents a novel approach to characterize the dynamics of the limit spectrum of large random matrices. This approach is based upon the notion we call "spectral dominance". In particular, we show that the limit spectral measure…
We consider complex sample covariance matrices $M_N=\frac{1}{N}YY^*$ where $Y$ is a $N \times p$ random matrix with i.i.d. entries $Y_{ij}, 1\leq i\leq N, 1\leq j \leq p$ with distribution $F$. Under some regularity and decay assumption on…
We consider $N\times N$ symmetric or hermitian random matrices with independent, identically distributed entries where the probability distribution for each matrix element is given by a measure $\nu$ with a subexponential decay. We prove…
We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…
This paper is about the relation of random matrix theory and the subordination phenomenon in complex analysis. We find that the resolvent of the sum of two random matrices is approximately subordinated to the resolvents of the original…
The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…