{"paper":{"title":"Identification of the Polaron measure in strong coupling and the Pekar variational formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chiranjib Mukherjee, S.R.S. Varadhan","submitted_at":"2018-12-17T18:00:16Z","abstract_excerpt":"The path measure corresponding to the Fr\\\"ohlich Polaron appearing in quantum statistical mechanics is defined as the tilted measure $$ \\widehat{\\mathbb P}_{\\varepsilon,T}= \\frac{1}{Z(\\varepsilon,T)}\\exp\\bigg(\\frac{1}{2}\\int_{-T}^T\\int_{-T}^T \\frac{\\varepsilon\\mathrm e^{-\\varepsilon |t-s|}}{|\\omega(t)-\\omega(s)|} \\mathrm d s \\,\\mathrm d t\\bigg)\\mathrm d\\mathbb P. $$ Here $\\varepsilon>0$ is the Kac parameter (or the inverse-coupling), and $\\mathbb P$ is the law of $3d$ Brownian increments. In [13] it was shown that the (thermodynamic) limit $\\lim_{T\\to\\infty}\\widehat{\\mathbb P}_{\\varepsilon,T}="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06927","kind":"arxiv","version":3},"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/1812.06927/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"}