Quantitative propagation of chaos in total variation for unregularized Vlasov-Riesz-Fokker-Planck systems

Abstract

We prove quantitative propagation of chaos in total variation for the unregularized repulsive Vlasov--Riesz--Fokker--Planck system on 𝕋^d and ℝ^d, d≥2. For product initial data and potentials with singularity |x|^−s, 0<s<d/2, we obtain an algebraic convergence rate for the k-particle marginals on a time interval independent of the particle number. The constants grow at most exponentially in k. The three-dimensional Coulomb case gives every rate N^−b with 0<b<1/3. The assumptions on its limiting solution hold for weighted Sobolev data with a Gaussian velocity moment and, on ℝ³, a polynomial spatial moment. The proof combines conditioning of the initial product law, auxiliary particle equations, and weighted BBGKY estimates. An L¹ estimate and pointwise exponential energy bounds control the remainder flux in weighted L^q. For correlated initial data satisfying pointwise energy and marginal error bounds, the comparison extends to 0<s<d−1.

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BibTeX RIS

BibTeX

@misc{jiang2026quantitative,
  title = {{Quantitative propagation of chaos in total variation for unregularized Vlasov-Riesz-Fokker-Planck systems}},
  author = {Ning Jiang and Juntao Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.23709},
  eprint = {2609.23709},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23709},
}

RIS

TY  - UNPB
TI  - Quantitative propagation of chaos in total variation for unregularized Vlasov-Riesz-Fokker-Planck systems
AU  - Ning Jiang
AU  - Juntao Wu
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.23709
UR  - https://arxiv.org/abs/2609.23709
AB  - We prove quantitative propagation of chaos in total variation for the unregularized repulsive Vlasov--Riesz--Fokker--Planck system on 𝕋^d and ℝ^d, d≥2. For product initial data and potentials with singularity |x|^−s, 0<s<d/2, we obtain an algebraic convergence rate for the k-particle marginals on a time interval independent of the particle number. The constants grow at most exponentially in k. The three-dimensional Coulomb case gives every rate N^−b with 0<b<1/3. The assumptions on its limiting solution hold for weighted Sobolev data with a Gaussian velocity moment and, on ℝ^3, a polynomial spatial moment. The proof combines conditioning of the initial product law, auxiliary particle equations, and weighted BBGKY estimates. An L^1 estimate and pointwise exponential energy bounds control the remainder flux in weighted L^q. For correlated initial data satisfying pointwise energy and marginal error bounds, the comparison extends to 0<s<d−1.
ER  -

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