Multifractality and statistical localization in highly heterogeneous random networks

Abstract

We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk. We study the structure of the eigenvectors associated with this divergence and find that they are multifractal with the statistics of eigenvector elements matching those of the resolvent entries. The corresponding localization mechanism relies on the statistical properties of the nodes rather than on any spatial structure around a localization centre. This "statistical localization" mechanism is potentially relevant for explaining localization in different models that display singularities in the bulk of the spectrum of eigenvalues

arXiv commentAccepted for publication in Europhysics Letters (EPL)

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Cited by in corpus (5)

• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Emergent multifractality in power-law decaying eigenstates
• Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
• Effects of clustering heterogeneity on the spectral density of sparse networks
• Soft modes in vector spin glass models on sparse random graphs