Cavity approach to the spectral density of sparse symmetric random matrices.

@article{Rogers2008CavityAT,
  title={Cavity approach to the spectral density of sparse symmetric random matrices.},
  author={Tim Rogers and Isaac P{\'e}rez Castillo and Reimer K{\"u}hn and Koujin Takeda},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2008},
  volume={78 3 Pt 1},
  pages={
          031116
        }
}
The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally treelike, and sparse covariance matrices. We derive a closed set of equations from which the density of eigenvalues can be efficiently calculated. Within this approach, the Wigner semicircle law for Gaussian matrices and the Marcenko-Pastur law for covariance matrices are recovered easily. Our results are compared… CONTINUE READING

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