منابع مشابه
Large Deviations from the Circular Law
We prove a full large deviations principle in the scale N for the empirical measure of the eigenvalues of an N N non self adjoint matrix composed of i i d zero mean random variables with variance N The good rate function which governs this rate func tion possesses as unique minimizer the circular law providing an alter native proof of convergence to the latter The techniques are related to rece...
متن کامل3 Deviations from the Circular Law
Consider Ginibre's ensemble of N × N non-Hermitian random matrices in which all entries are independent complex Gaussians of mean zero and variance 1 N. As N ↑ ∞ the normalized counting measure of the eigenvalues converges to the uniform measure on the unit disk in the complex plane. In this note we describe fluctuations about this Circular Law. First we obtain finite N formulas for the covaria...
متن کاملComplex Hermite Polynomials: from the Semi-circular Law to the Circular Law
We study asymptotics of orthogonal polynomial measures of the form |HN |2dγ where HN are real or complex Hermite polynomials with respect to the Gaussian measure γ. By means of differential equations on Laplace transforms, interpolation between the (real) arcsine law and the (complex) uniform distribution on the circle is emphasized. Suitable averages by an independent uniform law give rise to ...
متن کاملAround the circular law
These expository notes are centered around the circular law theorem, which states that the empirical spectral distribution of a n×n random matrix with i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the complex plane as the dimension n tends to infinity. This phenomenon is the non-Hermitian counterpart of the semi circular limit for Wigner random Hermitian matrices, ...
متن کاملOn the Circular Law
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent real entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the unit disc without assumptions on the existence of a density for the distribution of entries. We assume however that the entries have sub-Gaussian tails or ...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2004
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-004-0355-x