On the Circular Law

Details On the Circular Law On the Circular Law

2007-02-13

arxiv.org/abs/math/0702386v1

Mathematics

Probability

Scientific paper

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 are sparsely non-zero.

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