منابع مشابه
Eigenvectors of random matrices: A survey
Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on properties of eigenvectors when the matrix (or graph) is random.
متن کاملDelocalization of Eigenvectors of Random Matrices with Independent Entries
We prove that an n× n random matrix G with independent entries is completely delocalized. Suppose the entries of G have zero means, variances uniformly bounded below, and a uniform tail decay of exponential type. Then with high probability all unit eigenvectors of G have all coordinates of magnitude O(n−1/2), modulo logarithmic corrections. This comes a consequence of a new, geometric, approach...
متن کاملAccurate Eigenvectors of Oscillatory Matrices
The purpose of this report is to investigate the possibilities for accurate computation of eigenvectors of (unsymmetric) oscillatory matrices. The goal is to decide what “accurate” means, to determine whether the eigenvectors are determined “accurately” in that sense, and to engineer algorithms that will guarantee that accuracy. It is desirable for the computed eigenvector matrix to inherit the...
متن کاملDensity 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.
متن کاملCorrelations of eigenvectors for non-Hermitian random-matrix models.
We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for non-Hermitian random-matrix models in the large-N limit. We apply this result to a number of non-Hermitian random-matrix models and show that the outcome is in good agreement with numerical results.
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2018
ISSN: 1083-589X
DOI: 10.1214/18-ecp171