Related papers: Solvable Families of Random Block Tridiagonal Matr…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
Noncolliding diffusion processes reported in the present paper are $N$-particle systems of diffusion processes in one-dimension, which are conditioned so that all particles start from the origin and never collide with each other in a finite…
Block Toeplitz and Hankel matrices arise in many aspects of applications. In this paper, we will research the distributions of eigenvalues for some models and get the semicircle law. Firstly we will give trace formulae of block Toeplitz and…
Symmetric tridiagonal matrices appear ubiquitously in mathematical physics, serving as the matrix representation of discrete random Schr\"odinger operators. In this work we investigate the top eigenvalue of these matrices in the large…
The article discusses the matrices of the three forms whose inversions are: tridiagonal matrix, banded matrix or block-tridiagonal matrix and their relationships with the covariance matrices of measurements of ordinary (simple) Markov…
First, we consider a nonnegative homogeneous block tri-diagonal matrix and obtain its convergence parameter, where some results in the field of matrix analytic method are extended to the case where block matrices have countably infinite…
We derive conditions on the products of stochastic matrices guaranteeing the existence of a unique limit invariant distribution. Belying our approach is the hereby defined notion of restricted triangulated Laman graphs. The main idea is the…
Random Matrix Theory (RMT) has successfully modeled diverse systems, from energy levels of heavy nuclei to zeros of $L$-functions. Many statistics in one can be interpreted in terms of quantities of the other; for example, zeros of…
Assume a finite set of complex random variables form a determinantal point process, we obtain a theorem on the limit of the empirical distribution of these random variables. The result is applied to %We study the limits of the empirical…
Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower…
Structural properties of large random maps and lambda-terms may be gleaned by studying the limit distributions of various parameters of interest. In our work we focus on restricted classes of maps and their counterparts in the…
We describe some numerical experiments which determine the degree of spectral instability of medium size randomly generated matrices which are far from self-adjoint. The conclusion is that the eigenvalues are likely to be intrinsically…
We consider $N\times N$ Hermitian or symmetric random matrices with independent entries. The distribution of the $(i,j)$-th matrix element is given by a probability measure $\nu_{ij}$ whose first two moments coincide with those of the…
We introduce a symmetric tridiagonal matrix-valued process ($\beta$-TMP) $H(t)$ whose diagonal entries $H_{k,k}(t)$ evolve independently via an Ornstein-Uhlenbeck process starting at the origin and the off-diagonal entries $H_{k,k+1}(t)$…
Evaluation of the eigenvectors of symmetric tridiagonal matrices is one of the most basic tasks in numerical linear algebra. It is a widely known fact that, in the case of well separated eigenvalues, the eigenvectors can be evaluated with…
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…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
Random tensor models have applications in a variety of fields, such as quantum gravity, quantum information theory, mathematics of modern technologies, etc., and studying their statistical properties, e.g., tensor eigenvalue/vector…
Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of…
In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…