On the Spectrum of Random Anti-symmetric and Tournament Matrices

Michael Damron Georgia Tech Jack Hanson CUNY Philippe Sosoe Harvard University CMSA

Publications of CMSA of Harvard mathscidoc:1702.38045

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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@inproceedings{michaelon,
  title={On the Spectrum of Random Anti-symmetric and Tournament Matrices},
  author={Michael Damron, Jack Hanson, and Philippe Sosoe},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207033020835451245},
}
Michael Damron, Jack Hanson, and Philippe Sosoe. On the Spectrum of Random Anti-symmetric and Tournament Matrices. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207033020835451245.
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