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The limit empirical spectral distribution of complex matrix polynomials
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We study the empirical spectral distribution (ESD) for complex n x n matrix polynomials of degree k. We obtain exact formulae for the almost sure limit of the ESD in two distinct scenarios: (1) n -> \infty with k constant and (2) k -> \infty with n bounded by O(k^P) for some P>0. The main tools used are the logarithmic potential of some measure related to the matrix polynomial, and some classical estimates on the singular values of full random matrices with i.i.d. entries.
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Cited by 1 Pith paper
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Logarithmic Spectral Distribution of a Non-Hermitian $\beta$-Ensemble
The limiting spectral density of the new non-Hermitian beta-ensemble is the logarithm of the radius plus a constant, rotationally invariant on a compact disk.
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