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The circular law for random band matrices with arbitrary doubly stochastic variance profiles
We study the circular law for non-Hermitian random band matrices with independent entries and arbitrary doubly stochastic variance profiles. For matrices of size $n$ and bandwidth $n^γ$, we prove the circular law when $γ>\frac{5}{6}$ for Gaussian entries, or $γ>\frac{8}{9}$ for subgaussian entries u
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