منابع مشابه
The local circular law II: the edge case
In the first part of this article [8], we proved a local version of the circular law up to the finest scale N−1/2+ε for non-Hermitian random matrices at any point z ∈ C with ||z| − 1| > c for any c > 0 independent of the size of the matrix. Under the main assumption that the first three moments of the matrix elements match those of a standard Gaussian random variable after proper rescaling, we ...
متن کاملLocal Circular Law for Random Matrices
The circular law asserts that the spectral measure of eigenvalues of rescaled random matrices without symmetry assumption converges to the uniform measure on the unit disk. We prove a local version of this law at any point z away from the unit circle. More precisely, if ||z| − 1| > τ for arbitrarily small τ > 0, the circular law is valid around z up to scale N−1/2+ε for any ε > 0 under the assu...
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 ...
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 ...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2013
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-013-0539-3