Fluctuations and large deviations of some perturbed random matrices
نویسنده
چکیده
General statement of the problem. The following algebraic problem is very classical: Let A and B be two Hermitian matrices of the same size. Assume we know the spectrum of each of them. What can be said about the spectrum of their sum A + B? The problem was posed by Weyl [1912]. He gave a series of necessary conditions, known as Weyl’s interlacing inequalities: if λ1(A)≥ · · · ≥ λn(A), λ1(B)≥ · · · ≥ λn(B) and λ1(A+ B)≥ · · · ≥ λn(A+ B) are the spectra of A, B and A+ B, then
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تاریخ انتشار 2014