# Condensed Matter > Disordered Systems and Neural Networks

arXiv:1701.01484 (cond-mat)

# Title:Diluted banded random matrices: Scaling behavior of eigenfunction and spectral properties

Abstract: We demonstrate that the normalised localization length $\beta$ of the eigenfunctions of diluted (sparse) banded random matrices follows the scaling law $\beta=x^*/(1+x^*)$. The scaling parameter of the model is defined as $x^*\propto(b_{eff}^2/N)^\delta$, where $b_{eff}$ is the average number of non-zero elements per matrix row, $N$ is the matrix size, and $\delta\sim 1$. Additionally, we show that $x^*$ also scales the spectral properties of the model (up to certain sparsity) characterized by the spacing distribution of eigenvalues.
 Comments: 6 pages, 3 figures. arXiv admin note: text overlap with arXiv:1611.06695 Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn) DOI: 10.1088/1751-8121/aa9509 Cite as: arXiv:1701.01484 [cond-mat.dis-nn] (or arXiv:1701.01484v1 [cond-mat.dis-nn] for this version)

## Submission history

From: J. A. Mendez-Bermudez [view email]
[v1] Thu, 5 Jan 2017 21:28:02 UTC (1,040 KB)
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