Support convergence in the single ring theorem

Details Support convergence in the single ring theorem Support convergence in the single ring theorem

2010-12-13

arxiv.org/abs/1012.2624v1

Mathematics

Probability

Scientific paper

We study the eigenvalues of non-normal square matrices of the form
A_n=U_nT_nV_n with U_n,V_n independent Haar distributed on the unitary group
and T_n real diagonal. We show that when the empirical measure of the
eigenvalues of T_n converges, and T_n satisfies some technical conditions, all
these eigenvalues lie in a single ring.

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