منابع مشابه
The single ring theorem
Abstract We study the empirical measure LAn of the eigenvalues of non-normal square matrices of the form An = UnTnVn with Un,Vn independent Haar distributed on the unitary group and Tn real diagonal. We show that when the empirical measure of the eigenvalues of Tn converges, and Tn satisfies some technical conditions, LAn converges towards a rotationally invariant measure μ on the complex plane...
متن کاملSupport convergence in the single ring theorem
In [6], M. Krishnapur and the authors considered the convergence of the empricial measure of (complex) eigenvalues of matrices of the form An = TnUn, where Un is Haar distributed on U(n), the unitary group of n×n matrices, and independent of the self-adjoint matrix Tn (which therefore can be assumed diagonal, with real non-negative entries s i ). That is, with λ (n) i denoting the eigenvalues o...
متن کاملThe Merkuriev-suslin Theorem for Any Semi-local Ring
We introduce here a method which uses étale neighborhoods to extend results from smooth semi-local rings to arbitrary semi-local rings A by passing to the henselization of a smooth presentation of A. The technique is used to show that étale cohomology of A agrees with Galois cohomology, the Merkuriev-Suslin theorem holds for A, and to describe torsion in K2(A). We introduce here a method which ...
متن کامل‘‘Single ring theorem’’ and the disk-annulus phase transition
Recently, an analytic method was developed to study in the large N limit nonHermitian random matrices that are drawn from a large class of circularly symmetric non-Gaussian probability distributions, thus extending the existing Gaussian non-Hermitian literature. One obtains an explicit algebraic equation for the integrated density of eigenvalues from which the Green’s function and averaged dens...
متن کاملFluctuations for Analytic Test Functions in the Single Ring Theorem
We consider a non-Hermitian random matrix A whose distribution is invariant under the left and right actions of the unitary group. The so-called Single Ring Theorem, proved by Guionnet, Krishnapur and Zeitouni [31], states that the empirical eigenvalue distribution of A converges to a limit measure supported by an annulus S. In this text, we establish the convergence in distribution of random v...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2019
ISSN: 0091-1798
DOI: 10.1214/18-aop1284