Pith Number

pith:YI3YOOBD

pith:2026:YI3YOOBDFSV2YQQ6MCW2XLNDNC

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Nesterov acceleration for the Wasserstein minimization of displacement-convex free energies

Pierre Monmarch\'e

The mean-field underdamped Langevin process achieves Nesterov acceleration for Wasserstein minimization of displacement-convex free energies.

arxiv:2605.13186 v1 · 2026-05-13 · math.AP · math.OC · math.PR

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Claims

C1strongest claim

The mean-field underdamped Langevin process achieves a Nesterov acceleration with respect to the Wasserstein gradient flow of a displacement-convex free energy, in the sense that it converges at a rate of order given by the square-root of the Polyak-Łojasiewicz constant of the free energy.

C2weakest assumption

The free energy must be displacement-convex and satisfy a Polyak-Łojasiewicz inequality; the nonlinear extension relies on the linear-case breakthrough in [42] carrying over without additional obstructions.

C3one line summary

Mean-field underdamped Langevin dynamics achieve Nesterov acceleration for Wasserstein gradient flows of displacement-convex free energies.

References

67 extracted · 67 resolved · 3 Pith anchors

[1] Vari- ational methods for the kinetic fokker–planck equation.Analysis & PDE, 17(6):1953– 2010, 2024 1953

[2] Shifted composition iv: toward ballistic acceleration for log-concave sampling.arXiv preprint arXiv:2506.23062, 2025 2025

[3] Springer Science & Business Media, 2005 2005

[4] Hypocoercivity of piecewise deterministic markov process-monte carlo.The Annals of Applied Probability, 31(5):2478–2517, 2021 2021

[5] Maximum mean discrep- ancy gradient flow.Advances in neural information processing systems, 32, 2019 2019

Receipt and verification

First computed	2026-05-18T03:08:56.226427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2378738232cabac421e60adabada368b5f1c1251e3c3bed93272875e0ba03aa

Aliases

arxiv: 2605.13186 · arxiv_version: 2605.13186v1 · doi: 10.48550/arxiv.2605.13186 · pith_short_12: YI3YOOBDFSV2 · pith_short_16: YI3YOOBDFSV2YQQ6 · pith_short_8: YI3YOOBD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YI3YOOBDFSV2YQQ6MCW2XLNDNC \
  | 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: c2378738232cabac421e60adabada368b5f1c1251e3c3bed93272875e0ba03aa

Canonical record JSON

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      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T08:43:27Z",
    "title_canon_sha256": "233883b905d4a50683130cad2a8e7468855d303829a81ad09d679dc8802b0db5"
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  "source": {
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    "kind": "arxiv",
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}