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Cavity approach to the spectral density of sparse symmetric random matrices


Reference:

Rogers, T., Takeda, K., Pérez Castillo, I. and Kühn, R., 2008. Cavity approach to the spectral density of sparse symmetric random matrices. Physical Review E, 78 (3), 031116.

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Official URL:

http://dx.doi.org/10.1103/PhysRevE.78.031116

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Abstract

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 tree-like, 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 with numerical diagonalization, finding excellent agreement.

Details

Item Type Articles
CreatorsRogers, T., Takeda, K., Pérez Castillo, I. and Kühn, R.
DOI10.1103/PhysRevE.78.031116
Related URLs
URLURL Type
http://arxiv.org/abs/0803.1553Free Full-text
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code32170

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