{"paper":{"title":"VRJP recurrence and fractional-moment decay for the \\(H^{2|2}\\) model's effective field on the hierarchical lattice","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Jinglin Wang, Xiaolin Zeng","submitted_at":"2025-05-02T15:09:05Z","abstract_excerpt":"We prove recurrence of the vertex-reinforced jump process on the hierarchical lattice for spectral dimension \\(d<2\\) for every value of the conductance parameter \\(\\overline{W}\\), and at the critical spectral dimension \\(d=2\\) for sufficiently strong reinforcement, i.e., sufficiently small \\(\\overline{W}\\). The key estimate is a fractional-moment bound for the Green's function of the associated random Schr\\\"odinger operator, expressed as geometric decay across hierarchical scales for the effective \\(H^{2|2}\\) field. The proof combines the fractional-moment method with an exact hierarchical coa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.01337","kind":"arxiv","version":3},"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/2505.01337/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"}