{"paper":{"title":"Invariant Gibbs measures and global dynamics for fractional cubic Schr\\\"odinger equations on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chenyuan Zhang, Haitian Yue, Lifeng Zhao, Yuzhao Wang","submitted_at":"2026-06-29T12:38:09Z","abstract_excerpt":"We consider the defocusing Wick-ordered cubic fractional nonlinear Schr\\\"odinger equation on the two-dimensional torus with dispersion relation $\\omega(k)=|k|^\\alpha$. In the weakly dispersive regime $\\frac{29}{15}<\\alpha<2$, we construct global dynamics for almost every initial datum with respect to the associated Gibbs measure as the limit of the finite-dimensional truncated flows and prove invariance of the Gibbs measure. The core of the proof is an almost sure local theory based on the method of random averaging operators (arXiv:1910.08492v2). The main new ingredients are fractional lattic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30223","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/2606.30223/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"}