{"paper":{"title":"DLR equations and rigidity for the Sine-beta process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Adrien Hardy, David Dereudre, Myl\\`ene Ma\\\"ida, Thomas Lebl\\'e","submitted_at":"2018-09-11T15:50:36Z","abstract_excerpt":"We investigate Sine$_\\beta$, the universal point process arising as the thermodynamic limit of the microscopic scale behavior in the bulk of one-dimensional log-gases, or $\\beta$-ensembles, at inverse temperature $\\beta>0$. We adopt a statistical physics perspective, and give a description of Sine$_\\beta$ using the Dobrushin-Lanford-Ruelle (DLR) formalism by proving that it satisfies the DLR equations: the restriction of Sine$_\\beta$ to a compact set, conditionally to the exterior configuration, reads as a Gibbs measure given by a finite log-gas in a potential generated by the exterior configu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03989","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/1809.03989/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"}