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The Elliptic Law
Published 29 Aug 2012 in math.PR and math.CO | (1208.5883v4)
Abstract: We show that, under some general assumptions on the entries of a random complex $n \times n$ matrix $X_n$, the empirical spectral distribution of $\frac{1}{\sqrt{n}} X_n$ converges to the uniform law of an ellipsoid as $n$ tends to infinity. This generalizes the well-known circular law in random matrix theory.
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