{"paper":{"title":"Identification of the Polaron measure I: Fixed coupling regime and the central limit theorem for large times","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Chiranjib Mukherjee, S.R.S. Varadhan","submitted_at":"2018-02-15T18:29:02Z","abstract_excerpt":"We consider the Fr\\\"ohlich model of the Polaron whose path integral formulation leads to the transformed path measure\n  $$\n  \\widehat{\\mathbb P}_{\\alpha,T}(\\mathrm d\\omega)= Z_{\\alpha,T}^{-1}\\,\\, \\exp\\bigg\\{\\frac{\\alpha}{2}\\int_{-T}^T\\int_{-T}^T\\frac{e^{-|t-s|}}{|\\omega(t)-\\omega(s)|} \\, d s \\, d t\\bigg\\}\\,\\mathbb P(\\mathrm d\\omega)\n  $$\n  with respect to $\\mathbb P$ which governs the law of the increments of the three dimensional Brownian motion on a finite interval $[-T,T]$, and $ Z_{\\alpha,T}$ is the partition function or the normalizing constant and $\\alpha>0$ is a constant. The Polaron me"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05696","kind":"arxiv","version":6},"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/1802.05696/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"}