Related papers: Perturbations of diagonal matrices by band random …
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In both cases we show that most of the eigenvalues of the perturbed matrix are very close to a circle with centre at the origin. In the…
Let $A$ be a permutation invariant random matrix and $B$ another random matrix. We give a quantitative bound on the difference between the diagonal of the resolvent of $A+B$ and the diagonal of the resolvent of the free sum with…
We study the spectrum of an asymmetric random matrix with block structured variances. The rows and columns of the random square matrix are divided into $D$ partitions with arbitrary size (linear in $N$). The parameters of the model are the…
We give formulas for the density of the measure of orthogonality for orthonormal polynomials with unbounded recurrence coefficients. The formulas involve limits of appropriately scaled Tur\'an determinants or Christoffel functions. Exact…
We carry out numerical investigations of the perturbations in Nflation models where the mass spectrum is generated by random matrix theory. The tensor-to-scalar ratio and non-gaussianity are already known to take the single-field values,…
Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the…
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…
The discretization of the density matrix is proposed as a nonlinear positive map for systems with continuous variables. This procedure is used to calculate the entanglement between two modes through different criteria, such as Tsallis…
We look into the fluctuations caused by disturbances in power systems. In the linearized system of the power systems, the disturbance is modeled by a Brownian motion process, and the fluctuations are described by the covariance matrix of…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
In distributed optimization or Nash-equilibrium seeking over directed graphs, it is crucial to find a matrix norm under which the disagreement of individual agents' states contracts. In existing results, the matrix norm is usually defined…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…