{"paper":{"title":"Strong coupling limit of the Polaron measure and the Pekar process","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":"2018-06-18T18:00:10Z","abstract_excerpt":"The {\\it{Polaron measure}} is defined as the transformed path measure\n  $$\\widehat{\\mathbb P}_{\\epsilon,T}= Z_{\\epsilon,T}^{-1}\\,\\, \\exp\\bigg\\{\\frac{1}{2}\\int_{-T}^T\\int_{-T}^T\\frac{\\epsilon\\e^{-\\epsilon|t-s|}}{|\\omega(t)-\\omega(s)|} \\,\\d s \\,\\d t\\bigg\\}\\d\\mathbb P$$ with respect to the law $\\mathbb P$ of three dimensional Brownian increments on a finite interval $[-T,T]$, and $ Z_{\\epsilon,T}$ is the partition function with $\\epsilon>0$ being a constant. The logarithmic asymptotic behavior of the partition function $Z_{\\epsilon,T}$ was analyzed in \\cite{DV83} showing that $$ g_0=\\lim_{\\epsilo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06865","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":""},"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"}