On the localization transition in symmetric random matrices

Details On the localization transition in symmetric random matrices On the localization transition in symmetric random matrices

2010-05-20

arxiv.org/abs/1005.3712v3

Phys. Rev. E 82, 031135 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 6 figures

Scientific paper

10.1103/PhysRevE.82.031135

We study the behaviour of the inverse participation ratio and the localization transition in infinitely large random matrices through the cavity method. Results are shown for two ensembles of random matrices: Laplacian matrices on sparse random graphs and fully-connected L\'evy matrices. We derive a critical line separating localized from extended states in the case of L\'evy matrices. Comparison between theoretical results and diagonalization of finite random matrices is shown.

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