Spectra of Sparse Random Matrices
arXiv:0803.2886 · doi:10.1088/1751-8113/41/29/295002
Abstract
We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by Rodgers and Bray. Due attention is payed to the issue of localization. Our approach is not restricted to matrices defined on graphs with Poissonian degree distribution. Matrices defined on regular random graphs or on scale-free graphs, are easily handled. We also look at matrices with row constraints such as discrete graph Laplacians. Our approach naturally allows to unfold the total density of states into contributions coming from vertices of different local coordination.
22 papges, 8 figures (one on graph-Laplacians added), one reference added, some typos eliminated
References in corpus (5)
- Cavity Approach to the Spectral Density of Sparse Symmetric Random Matrices
- Finitely coordinated models for low-temperature phases of amorphous systems
- Statistics of delta peaks in the spectral density of large random trees
- The polynomial error probability for LDPC codes
- Spectral properties of complex networks