Related papers: Numerical Methods for Eigenvalue Distributions of …
Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an…
We calculate analytically the probability of large deviations from its mean of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles. In particular, we show that the…
This paper is my contribution to the planned publication Recent Perspectives in Random Matrix Theory (Cambridge University Press). Addressed is the problem of computing spacing distributions in the bulk for the three symmetry classes…
Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices ($\beta$=2), supported by explicit…
We study the overlaps between right and left eigenvectors for random matrices of the spherical and truncated unitary ensembles. Conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent…
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…
We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…
We introduce a directed, weighted random graph model, where the edge-weights are independent and beta-distributed with parameters depending on their endpoints. We will show that the row- and column-sums of the transformed edge-weight matrix…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
We provide a graphical calculus for computing averages of tensor network diagrams with respect to the distribution of random vectors containing independent uniform complex phases. Our method exploits the order structure of the partially…
We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…
Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real…
We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power $\beta$ by the Vandermonde determinant) to all orders of 1/N expansion in the case where the limiting…
In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
As in random matrix theories, eigenvector/value distributions are important quantities of random tensors in their applications. Recently, real eigenvector/value distributions of Gaussian random tensors have been explicitly computed by…
We calculate the discrete moments of the characteristic polynomial of a random unitary matrix, evaluated a small distance away from an eigenangle. Such results allow us to make conjectures about similar moments for the Riemann zeta…
The eigenvalue distribution of Hoppe's two matrix model is investigated in detail as a function of the model's coupling. For small couplings it is a perturbed Wigner semicircle, while for large couplings it is a parabolic distribution which…
We study a family of distributions that arise in critical unitary random matrix ensembles. They are expressed as Fredholm determinants and describe the limiting distribution of the largest eigenvalue when the dimension of the random…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…