Circular law for random matrices with unconditional log-concave distribution
2015 ◽
Vol 17
(04)
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pp. 1550020
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Keyword(s):
We explore the validity of the circular law for random matrices with non-i.i.d. entries. Let M be an n × n random real matrix obeying, as a real random vector, a log-concave isotropic (up to normalization) unconditional law, with mean squared norm equal to n. The entries are uncorrelated and obey a symmetric law of zero mean and variance 1/n. This model allows some dependence and non-equidistribution among the entries, while keeping the special case of i.i.d. standard Gaussian entries, known as the real Ginibre Ensemble. Our main result states that as the dimension n goes to infinity, the empirical spectral distribution of M tends to the uniform law on the unit disc of the complex plane.
2017 ◽
Vol 06
(03)
◽
pp. 1750011
2009 ◽
Vol 46
(3)
◽
pp. 377-396
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2017 ◽
Vol 06
(03)
◽
pp. 1750012
◽
2013 ◽
Vol 02
(02)
◽
pp. 1250017
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1995 ◽
Vol 54
(2)
◽
pp. 295-309
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