Circular law, extreme singular values and potential theory

Guangming Pan and Wang Zhou

Journal of Multivariate Analysis, 2010, vol. 101, issue 3, 645-656

Abstract: Consider the empirical spectral distribution of complex random nxn matrix whose entries are independent and identically distributed random variables with mean zero and variance 1/n. In this paper, via applying potential theory in the complex plane and analyzing extreme singular values, we prove that this distribution converges, with probability one, to the uniform distribution over the unit disk in the complex plane, i.e. the well known circular law, under the finite fourth moment assumption on matrix elements.

Keywords: Circular; law; Largest; singular; value; Potential; Small; ball; probability; Smallest; singular; value (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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