Cavity approach to the spectral density of sparse symmetric random matrices

Timothy Rogers, Koujin Takeda, Isaac Pérez Castillo, Reimer Kühn

Research output: Contribution to journalArticle

63 Citations (Scopus)

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.
Original languageEnglish
Article number031116
Number of pages7
JournalPhysical Review E
Volume78
Issue number3
DOIs
Publication statusPublished - 2008

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Spectral Density
Random Matrices
Symmetric matrix
Covariance matrix
Cavity
Semicircle Law
Cavity Method
cavities
Diagonalization
Sparse matrix
Closed set
Ensemble
matrices
Eigenvalue
eigenvalues
Graph in graph theory

Cite this

Cavity approach to the spectral density of sparse symmetric random matrices. / Rogers, Timothy; Takeda, Koujin; Pérez Castillo, Isaac; Kühn, Reimer.

In: Physical Review E, Vol. 78, No. 3, 031116, 2008.

Research output: Contribution to journalArticle

Rogers, Timothy ; Takeda, Koujin ; Pérez Castillo, Isaac ; Kühn, Reimer. / Cavity approach to the spectral density of sparse symmetric random matrices. In: Physical Review E. 2008 ; Vol. 78, No. 3.
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