{"paper":{"title":"Ergodicity for the hyperbolic $P(\\Phi)_2$-model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Leonardo Tolomeo","submitted_at":"2023-10-03T16:35:19Z","abstract_excerpt":"We consider the problem of ergodicity for the $P(\\Phi)_2$ measure of quantum field theory under the flow of the singular stochastic (damped) wave equation $u_{tt} + u_t + (1-\\Delta) u + {:}\\,p(u)\\mspace{2mu}{:} = \\sqrt 2 \\xi$, posed on the two-dimensional torus $\\mathbb T^2$. We show that the $P(\\Phi)_2$ measure is ergodic, and moreover that it is the unique invariant measure for (the Markov process associated to) this equation which belongs to a fairly large class of probability measures over distributions.\n  The main technical novelty of this paper is the introduction of the new concepts of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.02190","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/2310.02190/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"}