{"paper":{"title":"Central limit theorem for Gibbs measures on path spaces including long range and singular interactions and homogenization of the stochastic heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chiranjib Mukherjee","submitted_at":"2017-06-28T16:10:55Z","abstract_excerpt":"We consider a class of Gibbs measures defined with respect to increments $\\{\\omega(t)-\\omega(s)\\}_{s<t}$ of $d$-dimensional Wiener measure, with the underlying Hamiltonian carrying interactions of the form $H(t-s,\\omega(t)-\\omega(s))$ that are invariant under uniform translations of paths. In such interactions we allow {\\it{long-range}} dependence in the time variable (including power law decay up to $t\\mapsto (1+t)^{-(2+\\varepsilon)}$ for $\\varepsilon>0$) and unbounded (singular) interactions (including singularities of the form $x\\mapsto 1/|x|^p$ in $d\\geq 3$ or $x\\mapsto \\delta_0(x)$ in $d="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09345","kind":"arxiv","version":5},"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/1706.09345/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"}