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 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...
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 کاملCommon fixed point theorem for nonexpansive type single valued mappings
The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of ...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2015
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-015-0632-x