The Elliptic Law

2012/08/31 by Hoi Nguyen, Sean O'Rourke · 1 citation
Mathematics · #math.PR #math.CO

paper · pdf

published as International Mathematics Research Notices Vol. 2015, No. 17 (2015), pp. 7620--7689 · 57 pages; minor corrections

arxiv created 2014/09/09 · arxiv updated 2016/01/29

Abstract

We show that, under some general assumptions on the entries of a random complex n × n matrix X_n, the empirical spectral distribution of (1)/(√(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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