{"paper":{"title":"Quantitative Edge Eigenvector Universality for Random Regular Graphs: Berry-Esseen Bounds with Explicit Constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.SP"],"primary_cat":"math.PR","authors_text":"Leonhard Nagel","submitted_at":"2025-07-16T05:31:51Z","abstract_excerpt":"We establish the first quantitative Berry-Esseen bounds for edge eigenvector statistics in random regular graphs. For any $d$-regular graph on $N$ vertices with fixed $d \\geq 3$ and deterministic unit vector $\\mathbf{q} \\perp \\mathbf{e}$, we prove that the normalized overlap $\\sqrt{N}\\langle \\mathbf{q}, \\mathbf{u}_2 \\rangle$ satisfies \\[ \\sup_{x \\in \\mathbb{R}} \\left|\\mathbb{P}\\left(\\sqrt{N}\\langle \\mathbf{q}, \\mathbf{u}_2 \\rangle \\leq x\\right) - \\Phi(x)\\right| \\leq C_d N^{-1/6+\\varepsilon} \\] where $\\mathbf{u}_2$ is the second eigenvector and $C_d \\leq \\tilde{C}d^3\\varepsilon^{-10}$ for an ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12502","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.12502/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"}