Distribution of the eigenvalues of random block-matrices

Distribution of Eigenvalues for Some Sets of Random Matrices

Asymptotic Distribution of Eigenvalues and Degeneration of Sparse Random Matrices

This work is concerned with an asymptotical distribution of eigenvalues of sparse random matrices. It is shown that the semicircle law which is known for random matrices is also valid for the sparse random matrices with sparsity nIN=o(1), where n is the matrix size and 2N the number of non-zero elements of the matrix. The degree of degeneration is also estimated for the matrices with 2N—cn (c>0...

Eigenvalues of Euclidean random matrices

We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of n random points in a compact set Ωn of R. Under various assumptions we establish the almost sure convergence of the limiting spectral measure as the number of points goes to infinity. The moments of the limiting distribution are computed, and we prove that t...

18.338: The Eigenvalues of Random Matrices Histogramming

We assume that the reader is familiar with the most basic of facts concerning continuous random variables or is willing to settle for the following sketchy description. Samples from a (univariate or multivariate) experiment can be histogrammed either in practice or as a thought experiment. Histogramming counts how many samples fall in a certain interval. Underlying is the notion that there is a...

Density of Eigenvalues of Random Normal Matrices

The relation between random normal matrices and conformal mappings discovered by Wiegmann and Zabrodin is made rigorous by restricting normal matrices to have spectrum in a bounded set. It is shown that for a suitable class of potentials the asymptotic density of eigenvalues is uniform with support in the interior domain of a simple smooth curve.