Pith Number

pith:L5OPJ2BG

pith:2026:L5OPJ2BGAAP46B4QADXF2YACAQ

not attested not anchored not stored refs resolved

The inertial It\^o drift and its applications to particle collision

Franco Flandoli, Mengzi Xie, Sandra Cerrai

The small-mass limit of inertial particles driven by Ornstein-Uhlenbeck forces produces an extra inertial Itô drift whose strength depends on the ratio of mass to correlation time.

arxiv:2605.13518 v1 · 2026-05-13 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L5OPJ2BGAAP46B4QADXF2YACAQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The small mass μ limit of an inertial system driven by an Ornstein Uhlenbeck fluid force, with correlation time ε going to zero, leads to a first order system with an additional drift, which we call inertial-Itô-drift, depending on the limit α of the ratio μ/ε; the drift being zero when α=0, corresponding to the Stratonovich integral in the limit equation, as in the Wong-Zakai theory.

C2weakest assumption

That the driving force is an Ornstein-Uhlenbeck process and that the double limit is taken with μ/ε → α, allowing the application of Wong-Zakai type results to the inertial system.

C3one line summary

The inertial Itô drift emerges in the limiting first-order equation for small-mass particles in Ornstein-Uhlenbeck driven flows, vanishing only for zero mass-to-correlation-time ratio and corresponding to Stratonovich calculus.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] J. Bec, K. Gustavsson, B. Mehlig,Statistical models for the dynamics of heavy particles in turbulence, Annu. Rev. Fluid Mech. 56 (2024), pp. 189–213 2024

[2] C. L. Berselli, T. Iliescu, J. W. Layton,Mathematics of Large Eddy Simulation of Turbulent Flows, Springer, 2006 2006

[3] Boussinesq,Essai sur la th´ eorie des eaux courantes, M´ emoires pr´ esent´ es par divers savants a l’Academie des Sciences de l’Institut National de France, XXIII (1), (1877)

[4] Cerrai,A Khasminskii type averaging principle for stochastic reaction-diffusion equations, Annals of Applied Probability 19 (2009), pp 2009

[5] F. De Lillo, M. Cencini, S. Musacchio, G. Boffetta,Clustering and turbophoresis in a shear flow without walls, Physics of Fluids 28 (2016) 2016

Receipt and verification

First computed	2026-05-18T02:44:24.414542Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f5cf4e826001fcf079000ee5d60020430f70e86c6ebbd71cdc502a7d4a9b151

Aliases

arxiv: 2605.13518 · arxiv_version: 2605.13518v1 · doi: 10.48550/arxiv.2605.13518 · pith_short_12: L5OPJ2BGAAP4 · pith_short_16: L5OPJ2BGAAP46B4Q · pith_short_8: L5OPJ2BG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L5OPJ2BGAAP46B4QADXF2YACAQ \
  | 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: 5f5cf4e826001fcf079000ee5d60020430f70e86c6ebbd71cdc502a7d4a9b151

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce9423eb565eccf84256f69fd89af5ba0a12c5d6af22f79500c72cb8f0995a7a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-13T13:35:17Z",
    "title_canon_sha256": "3a7a5cb96b6d1b28fd6e53ab76e5bbe109c012c953548cec1658fcbe8f26baf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13518",
    "kind": "arxiv",
    "version": 1
  }
}