“Single ring theorem” and the disk-annulus phase transition
نویسندگان
چکیده
منابع مشابه
‘‘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...
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I review aspects of work done in collaboration with A. Zee and R. Scalettar [1, 2, 3] on complex non-hermitean random matrices. I open by explaining why the bag of tools used regularly in analyzing hermitean random matrices cannot be applied directly to analyze non-hermitean matrices, and then introduce the Method of Hermitization, which solves this problem. Then, for rotationally invariant ens...
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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...
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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...
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This result has also been proved by Bowditch [2], using very different methods. We discuss these differences at the end of this introduction. The terminology used is standard (from [11] and [17]). The importance of splitting groups along infinite cyclic subgroups is well known from the work of Paulin [13], Rips and Sela [14] and Sela [18]. If G has an infinite cyclic subgroup H such that e(G,H)...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2001
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1412599