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Article Dans Une Revue Communications in Contemporary Mathematics Année : 2015

Circular law for random matrices with unconditional log-concave distribution

Résumé

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.
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Dates et versions

hal-00803841 , version 1 (23-03-2013)

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Radosław Adamczak, Djalil Chafai. Circular law for random matrices with unconditional log-concave distribution. Communications in Contemporary Mathematics, 2015, 17 (4), pp.1550020. ⟨hal-00803841⟩
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