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Cavity approach to the spectral density of sparse symmetric random matrices

Rogers, T (King's College, London)
Friday 18 July 2008, 16:45-17:30

Seminar Room 1, Newton Institute


In this talk the spectral density of the ensemble 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.


[pdf ]


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