{"paper":{"title":"Diluted banded random matrices: Scaling behavior of eigenfunction and spectral properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Francisco A. Rodrigues, Guilherme Ferraz de Arruda, J. A. Mendez-Bermudez, Yamir Moreno","submitted_at":"2017-01-05T21:28:02Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01484","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}