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- W3173817711 abstract "In this short note, we extend the celebrated results of Tao and Vu, and Krishnapur on the universality of empirical spectral distributions to a wide class of inhomogeneous complex random matrices, by showing that a technical and hard-to-verify Fourier domination assumption may be replaced simply by a natural uniform anti-concentration assumption. Along the way, we show that inhomogeneous complex random matrices, whose expected squared Hilbert-Schmidt norm is quadratic in the dimension, and whose entries (after symmetrization) are uniformly anti-concentrated at $0$ and infinity, typically have smallest singular value $Omega(n^{-1/2})$. The rate $n^{-1/2}$ is sharp, and closes a gap in the literature. Our proofs closely follow recent works of Livshyts, and Livshyts, Tikhomirov, and Vershynin on inhomogeneous real random matrices. The new ingredient is a couple of anti-concentration inequalities for sums of independent, but not necessarily identically distributed, complex random variables, which may also be useful in other contexts." @default.
- W3173817711 created "2021-07-05" @default.
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- W3173817711 date "2021-01-01" @default.
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- W3173817711 title "A note on the universality of ESDs of inhomogeneous random matrices" @default.
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- W3173817711 doi "https://doi.org/10.30757/alea.v18-39" @default.
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