The Elliptic Law

By Hoi H. Nguyen, Sean O’Rourke. 2012

133 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/76763c323ed523a2621dbc9da18d693d34df4964

How researchers see this paper

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In Mathematical Physics

1. Stefano Allesina
2. Si Tang

In Statistics and Probability

1. Stefano Allesina
2. Si Tang

Citations in the corpus

• The stability–complexity relationship at age 40: a random matrix perspective (2015, background): “Recently (Naumov 2012; Nguyen and O’Rourke 2012), proofs of the universality of the elliptic law started appearing in the mathematical literature.”