Real spectra of large real asymmetric random matrices.

  title={Real spectra of large real asymmetric random matrices.},
  author={Wojciech Tarnowski},
  journal={Physical review. E},
  volume={105 1},
  • W. Tarnowski
  • Published 6 April 2021
  • Mathematics, Computer Science
  • Physical review. E
When a randomness is introduced at the level of real matrix elements, depending on its particular realization, a pair of eigenvalues can appear as real or form a complex conjugate pair. We show that in the limit of large matrix size the density of such real eigenvalues is proportional to the square root of the asymptotic density of complex eigenvalues continuated to the real line. This relation allows one to calculate the real densities up to a normalization constant, which is then applied to… 

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