Empirical spectral distribution of rescaled sparse row-regular 0-1 matrices converges in probability to the circular law when d = o(n) and d at least polylogarithmic.
Tao.Topics in random matrix theory, volume 132
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Dense random combinatorial matrices have smallest singular value typically of order n^{-1/2}.
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The circular law for sparse random combinatorial matrices
Empirical spectral distribution of rescaled sparse row-regular 0-1 matrices converges in probability to the circular law when d = o(n) and d at least polylogarithmic.
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An upper bound on the smallest singular value of dense random combinatorial matrices
Dense random combinatorial matrices have smallest singular value typically of order n^{-1/2}.