{"paper":{"title":"Tamed Feynman-Kac diffusion processes: Killing-branching intertwine","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Taming of Feynman-Kac kernels arises when negative potential regions introduce branching that counters killing in diffusion processes.","cross_cats":["math-ph","math.MP","math.PR","nlin.SI","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Mariusz \\.Zaba, Piotr Garbaczewski","submitted_at":"2026-05-08T14:53:10Z","abstract_excerpt":"Relaxation to equilibrium of a drifted Brownian motion is quantified by a probability density function, whose main (multiplicative) entry is an inferred Feynman-Kac kernel of the Schr\\\"{o}dinger semigroup operator. Although seemingly devoid of a natural probabilistic significance (except for its explicit path integral definition), the pertinent kernel relaxes to equilibrium as well. The implicit Feynman-Kac potential ${\\cal{V}}(x)$, continuous, confining and bounded from below, may take negative values. If positive, ${\\cal{V}}(x)$ can be interpreted as the killing rate of the decaying diffusio"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The taming inavoidably appears in conjunction with the existence of the negativity subdomains of V(x) in R. [...] the arising killed diffusion processes with branching, we interpret as the possible path-wise background of tamed (relaxing) Feynman-Kac diffusions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That computer-assisted path-wise arguments on a number of nonlinear 1D model systems suffice to establish consistency of the killing/branching taming scenario for general relaxing F-K kernels, especially beyond the semiclassical regime for double-well potentials.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Tamed relaxing Feynman-Kac diffusions emerge from killed-branching processes when the potential has negative subdomains, with consistency shown by simulations on 1D double-well models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Taming of Feynman-Kac kernels arises when negative potential regions introduce branching that counters killing in diffusion processes.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6ea1ae51a4ac3522bb72e1c325ba4dd9343c51942a79c221de6a7714a697b4f4"},"source":{"id":"2605.07824","kind":"arxiv","version":1},"verdict":{"id":"e9c8d1ea-06c4-4817-ab39-d4a26554a95b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-11T02:10:31.377931Z","strongest_claim":"The taming inavoidably appears in conjunction with the existence of the negativity subdomains of V(x) in R. [...] the arising killed diffusion processes with branching, we interpret as the possible path-wise background of tamed (relaxing) Feynman-Kac diffusions.","one_line_summary":"Tamed relaxing Feynman-Kac diffusions emerge from killed-branching processes when the potential has negative subdomains, with consistency shown by simulations on 1D double-well models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That computer-assisted path-wise arguments on a number of nonlinear 1D model systems suffice to establish consistency of the killing/branching taming scenario for general relaxing F-K kernels, especially beyond the semiclassical regime for double-well potentials.","pith_extraction_headline":"Taming of Feynman-Kac kernels arises when negative potential regions introduce branching that counters killing in diffusion processes."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.07824/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T10:02:13.923036Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T04:49:35.596935Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T15:31:18.764356Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T11:31:11.495988Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"63a822b173db76ccb353aa8b4ef3299822caa6671c93e08a41b44537e534525f"},"references":{"count":53,"sample":[{"doi":"","year":2000,"title":"How deep are the local minimum wells ? Improving the resolution ofq(t) = min[1,−V(X(t))δt]about the minima. The definition (44) ofV(α, x) =ax 2m−2 −bx m−2, witha=m 2α2/8,b=m(m−1)α/4,{α= 2,2/m,2m}, and","work_id":"1afb7be0-eb36-44d9-a56e-35bb0d0f9db7","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Deeply non-perturbative regime","work_id":"e97ae1f9-b3b1-4dfe-94af-8b4e3a50ca7a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"It is nowadays a widely accepted routine to employ the ”euclideanization” of otherwise intractable (mostly) quantum models","work_id":"bb43b014-a0ef-421f-8ee3-5b6e710c50d5","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Some explicit solutions of the Euler-Lagrange equations (20) with the double-well potentialV(x). 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