{"paper":{"title":"Fermionic Dyson expansions and stochastic Duistermaat-Heckman localization on loop spaces","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.KT","math.PR"],"primary_cat":"math.DG","authors_text":"Batu G\\\"uneysu, Jonas Miehe","submitted_at":"2024-10-17T21:14:20Z","abstract_excerpt":"Given a self-adjoint operator $H\\geq 0$ and (appropriate) densely defined and closed operators $P_{1},\\dots, P_{n}$ in a Hilbert space $\\mathscr{H}$, we provide a systematic study of bounded operators given by iterated integrals\n  \\begin{align}\\label{oh}\n  \\int_{\\{ 0\\leq s_1\\leq \\dots\\leq s_n\\leq t\\}}\\mathrm{e}^{-s_1H}P_{1}\\mathrm{e}^{-(s_2-s_1)H}P_{2}\\cdots \\mathrm{e}^{-(s_n-s_{n-1})H}P_{n} \\mathrm{e}^{-(t-s_n)H}\\, \\mathrm{d} s_{1} \\ldots \\mathrm{d} s_{n},\\quad t>0.\n  \\end{align} These operators arise naturally in noncommutative geometry and the geometry of loop spaces. Using Fermionic calcul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.14034","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/2410.14034/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"}