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Abstract: We study the behaviour of the inverse participation ratio and thelocalization transition in infinitely large random matrices through the cavitymethod. Results are shown for two ensembles of random matrices: Laplacianmatrices on sparse random graphs and fully-connected L\-evy matrices. We derivea critical line separating localized from extended states in the case of L\-evymatrices. Comparison between theoretical results and diagonalization of finiterandom matrices is shown.



Author: F. L. Metz, I. Neri, D. Bollé

Source: https://arxiv.org/







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