Equivalence of replica and cavity methods for computing spectra of sparse random matrices.
نویسنده
چکیده
We show by direct calculation that the replica and cavity methods are exactly equivalent for the spectrum of an Erdős-Rényi random graph. We introduce a variational formulation based on the cavity method and use it to find approximate solutions for the density of eigenvalues. We also use this variational method for calculating spectra of sparse covariance matrices.
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عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 83 1 Pt 1 شماره
صفحات -
تاریخ انتشار 2011