{"paper":{"title":"From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Davide Facoetti, Giulio Biroli, Pierpaolo Vivo","submitted_at":"2016-07-20T13:15:54Z","abstract_excerpt":"We study the statistics of the local resolvent and non-ergodic properties of eigenvectors for a generalised Rosenzweig-Porter $N\\times N$ random matrix model, undergoing two transitions separated by a delocalised non-ergodic phase. Interpreting the model as the combination of on-site random energies $\\{a_i\\}$ and a structurally disordered hopping, we found that each eigenstate is delocalised over $N^{2-\\gamma}$ sites close in energy $|a_j-a_i|\\leq N^{1-\\gamma}$ in agreement with Kravtsov \\emph{et al}, arXiv:1508.01714. Our other main result, obtained combining a recurrence relation for the res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05942","kind":"arxiv","version":2},"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"}