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Revisiting Toeplitz and Hankel random matrices via $*$-convergence of circulant-type matrices
We establish the joint $*$-convergence of a random circulant matrix and a specific deterministic diagonal matrix. We also show that the empirical spectral distributions of skew-circulant and left skew-circulant random matrices converge weakly a.s.~to complex Gaussian and symmetrized Rayleigh distrib
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