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Density of eigenvalues of random normal matrices. (English) Zbl 1129.82017

Summary: The relation between random normal matrices and conformal mappings discovered by P. B. Wiegmann and A. Zabrodin [Commun. Math. Phys. 213, 523–538 (2000; Zbl 0973.37042)] is made rigorous by restricting normal matrices to have spectrum in a bounded set. It is shown that for a suitable class of potentials the asymptotic density of eigenvalues is uniform with support in the interior domain of a simple smooth curve.

MSC:

82B44 Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
15B52 Random matrices (algebraic aspects)
62E20 Asymptotic distribution theory in statistics
30E05 Moment problems and interpolation problems in the complex plane

Citations:

Zbl 0973.37042
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References:

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