Pith Number

pith:TF4WVBMV

pith:2026:TF4WVBMVSPMFW5RVOXNF65CBEJ

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Tamed Feynman-Kac diffusion processes: Killing-branching intertwine

Mariusz \.Zaba, Piotr Garbaczewski

Taming of Feynman-Kac kernels arises when negative potential regions introduce branching that counters killing in diffusion processes.

arxiv:2605.07824 v1 · 2026-05-08 · cond-mat.stat-mech · math-ph · math.MP · math.PR · nlin.SI · quant-ph

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

53 extracted · 53 resolved · 0 Pith anchors

[1] 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 2000

[2] Deeply non-perturbative regime

[3] It is nowadays a widely accepted routine to employ the ”euclideanization” of otherwise intractable (mostly) quantum models

[4] Some explicit solutions of the Euler-Lagrange equations (20) with the double-well potentialV(x). Although no explicit imaginary time transformation has been ever involved in our discussion, it is wort

[5] Risken,The Fokker-Planck equation, (Springer, Berlin, 1992) 1992

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T01:03:32.740965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99796a859593d85b763575da5f7441224de5027ae977503fdd1db2f95f6538c3

Aliases

arxiv: 2605.07824 · arxiv_version: 2605.07824v1 · doi: 10.48550/arxiv.2605.07824 · pith_short_12: TF4WVBMVSPMF · pith_short_16: TF4WVBMVSPMFW5RV · pith_short_8: TF4WVBMV

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TF4WVBMVSPMFW5RVOXNF65CBEJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 99796a859593d85b763575da5f7441224de5027ae977503fdd1db2f95f6538c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b80820432670b6ea037c2d28f6a7199ea2e72190685713bc469dad49a9e2c5c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR",
      "nlin.SI",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-08T14:53:10Z",
    "title_canon_sha256": "57f2ec39f4b401121df5c157a0ca2de4563f271ef7e58d8d862d2b012ba822a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.07824",
    "kind": "arxiv",
    "version": 1
  }
}