Density of eigenvalues of random normal matrices
arXiv:math/0406604 · doi:10.1007/s00220-005-1372-z
Abstract
The relation between random normal matrices and conformal mappings discovered by Wiegmann and Zabrodin 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.
17 pages. Corrected version