A note on the universality of ESDs of inhomogeneous random matrices

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