{"paper":{"title":"Localization-delocalization transition for a random block matrix model at the edge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bertrand Stone, Fan Yang, Jiaqi Fan, Jun Yin","submitted_at":"2025-04-01T08:03:10Z","abstract_excerpt":"Consider a random block matrix model consisting of $D$ random systems arranged along a circle, where each system is modeled by an independent $N\\times N$ complex Hermitian Wigner matrix. Neighboring systems interact via an arbitrary deterministic $N\\times N$ matrix $A$. In this paper, we extend the localization-delocalization transition previously established in arxiv:2312.07297 for the bulk eigenvalue spectrum to the entire spectrum, including the spectral edges. Let $[E^-,E^+]$ denote the support of the limiting spectral density, and define $\\kappa_E:=|E-E^+|\\wedge |E-E^-|$ as the distance f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.00512","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.00512/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}