Empirical spectral distributions of arbitrary-degree polynomials in Ginibre matrices converge to their Brown measures as matrix size tends to infinity.
The limiting spectral law for sparse iid matrices
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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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Brown measure convergence for the spectrum of polynomials in Ginibre matrices
Empirical spectral distributions of arbitrary-degree polynomials in Ginibre matrices converge to their Brown measures as matrix size tends to infinity.
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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.