Pith Number

pith:6IQKAGSL

pith:2024:6IQKAGSLQFTZF44YTZF46NJNXB

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Symmetries for the gKPZ equation via multi-indices

Carlo Bellingeri, Yvain Bruned

Multi-indices compute the exact dimensions of the two symmetry spaces for the generalised KPZ equation by avoiding over-parametrization of renormalised terms.

arxiv:2410.00834 v3 · 2024-10-01 · math.PR · math.AP · math.RA

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Claims

C1strongest claim

We consider the equation in the full-subcritical regimes and use multi-indices that avoid an over-parametrization of the renormalised equation to compute the dimension of the two spaces associated with these two symmetries. Our proof is quite elementary and shows that multi-indices provide in this case a simplification in comparison to the results obtained via decorated trees.

C2weakest assumption

Multi-indices can be defined and manipulated so that they label renormalized terms without introducing over-parametrization, allowing direct dimension counts of the symmetry spaces that match the structure of the gKPZ equation (abstract, paragraph on multi-indices).

C3one line summary

Computes dimensions of symmetry spaces for the gKPZ equation via multi-indices that avoid over-parametrization, providing an elementary proof that simplifies prior decorated-tree results and completes the chain-rule program.

References

42 extracted · 42 resolved · 3 Pith anchors

[1] I. Bailleul, Y. Bruned Locality for singular stochastic PDEs. arXiv:2109.00399

[2] I. Bailleul, Y. Bruned Random models for singular SPDEs. arXiv:2301.09596

[3] Bellingeri An Itˆo type formula for the additive stochastic heat equation 2020 · doi:10.1214/19-ejp404/25

[4] Y. Bruned, A. Chandra, I. Chevyrev, M. Hairer. Renormalising SPDEs in regularity structures. J. Eur. Math. Soc. (JEMS), 23, no. 3, (2021), 869-947. doi:10.4171/ JEMS/1025 2021

[5] Y. Bruned, V. Dotsenko. Novikov algebras and multi-indices in regularity structures arXiv:2311.09091

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Cited by

1 paper in Pith

Cancellations for dispersive PDEs with random initial data

Receipt and verification

First computed	2026-05-26T02:03:47.083125Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f220a01a4b816792f3989e4bcf352db86479d2fa5c6c18cd74cd2481f7222e00

Aliases

arxiv: 2410.00834 · arxiv_version: 2410.00834v3 · doi: 10.48550/arxiv.2410.00834 · pith_short_12: 6IQKAGSLQFTZ · pith_short_16: 6IQKAGSLQFTZF44Y · pith_short_8: 6IQKAGSL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6IQKAGSLQFTZF44YTZF46NJNXB \
  | 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: f220a01a4b816792f3989e4bcf352db86479d2fa5c6c18cd74cd2481f7222e00

Canonical record JSON

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      "math.AP",
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-10-01T16:14:21Z",
    "title_canon_sha256": "f929842d522a3de2428f261899c657ba44b7b815df264bc2ea359f5c5d84a71b"
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