Philippe SosoeHarvard University CMSAUzy SmilanskyWeizmann Institute
Publications of CMSA of Harvardmathscidoc:1702.38044
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.
@inproceedings{philippeon,
title={On the Spectrum of Random Anti-symmetric and Tournament Matrices},
author={Philippe Sosoe, and Uzy Smilansky},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207032745406359244},
}
Philippe Sosoe, and Uzy Smilansky. On the Spectrum of Random Anti-symmetric and Tournament Matrices. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207032745406359244.