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.

Related documents:

Official URL:

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

Related URLs:

• http://arxiv.org/abs/0803.1553

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.

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