Equivalence of replica and cavity methods for computing spectra of sparse random matrices

Details Equivalence of replica and cavity methods for computing spectra of sparse random matrices Equivalence of replica and cavity methods for computing spectra of sparse random matrices

2011-05-25

arxiv.org/abs/1105.5047v1

Phys. Rev. E 83, 011118 (2011)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.83.011118

We show by direct calculation that the replica and cavity methods are exactly
equivalent for the spectrum of Erdos-Renyi 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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