On the spectrum of random anti-symmetric and tournament matrices
2016 ◽
Vol 05
(03)
◽
pp. 1650010
We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the non-Hermitian matrix around any fixed index are interlaced with those of the anti-symmetric matrix. Along the way, we show that some tools recently developed to study the eigenvalue distributions of Hermitian matrices extend to the anti-symmetric setting.
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1997 ◽
Vol 53
(1-3)
◽
pp. 88-94
◽
2005 ◽
Vol 55
(6)
◽
pp. 1943-2000
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