Circular law, extreme singular values and potential theory
نویسندگان
چکیده
منابع مشابه
Circular law, extreme singular values and potential theory
Consider the empirical spectral distribution of complex random n×n 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 dis...
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Consider the empirical spectral distribution of complex random n×n 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 dis...
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The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to information theory operate with random matrices in fixed dimensions. This survey addresses the non-asymptotic theory of extreme singular values of random matrices w...
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Dedicated to Professor H. M. Srivastava on the Occasion of his Seventieth Birth Anniversary
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2010
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2009.08.005