The Local Semicircle Law for Random Matrices with a Fourfold Symmetry

@article{Alt2015TheLS,
  title={The Local Semicircle Law for Random Matrices with a Fourfold Symmetry},
  author={Johannes Alt},
  journal={arXiv: Mathematical Physics},
  year={2015}
}
  • Johannes Alt
  • Published 2015
  • Mathematics, Physics
  • arXiv: Mathematical Physics
We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally arises as the Fourier transform of a Gaussian orthogonal ensemble (GOE). It also occurs as the flip matrix model - an approximation of the two-dimensional Anderson model at small disorder. We show that the density of states converges to the Wigner… Expand
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