Quantitative propagation of chaos on arbitrary finite time intervals for the three-dimensional repulsive Vlasov-Poisson-Fokker-Planck equation
Abstract
We prove quantitative propagation of chaos in total variation for repulsive Vlasov--Riesz--Fokker--Planck (VRFP) equations on 𝕋d and ℝd with unregularized interaction potentials with singularity |x|−s, 0<s<d/2. On every finite time interval on which the limiting classical solution satisfies the stated regularity assumptions, the particle marginals with a product initial law converge at an algebraic rate in the particle number, with constants growing at most exponentially in the marginal order. For the three-dimensional repulsive Vlasov--Poisson--Fokker--Planck (VPFP) equation on ℝ3, a weighted Cm initial probability density, m≥3, with Gaussian velocity decay and polynomial spatial decay of order M>3 gives convergence to the global classical solution on every finite time interval. The proof combines conditioning of the initial product law with weighted BBGKY estimates. A decomposition of the potential and a bounded modification of the far-field force yield weighted bounds growing geometrically in the marginal order on the prescribed interval. A centered second-moment estimate permits summation of the error hierarchy, and a synchronous coupling transfers the estimate to the original dynamics.
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BibTeX
@misc{jiang2026quantitative,
title = {{Quantitative propagation of chaos on arbitrary finite time intervals for the three-dimensional repulsive Vlasov-Poisson-Fokker-Planck equation}},
author = {Ning Jiang and Juntao Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40422},
eprint = {2610.40422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40422},
}
RIS
TY - UNPB
TI - Quantitative propagation of chaos on arbitrary finite time intervals for the three-dimensional repulsive Vlasov-Poisson-Fokker-Planck equation
AU - Ning Jiang
AU - Juntao Wu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40422
UR - https://arxiv.org/abs/2610.40422
AB - We prove quantitative propagation of chaos in total variation for repulsive Vlasov--Riesz--Fokker--Planck (VRFP) equations on 𝕋^d and ℝ^d with unregularized interaction potentials with singularity |x|^−s, 0<s<d/2. On every finite time interval on which the limiting classical solution satisfies the stated regularity assumptions, the particle marginals with a product initial law converge at an algebraic rate in the particle number, with constants growing at most exponentially in the marginal order. For the three-dimensional repulsive Vlasov--Poisson--Fokker--Planck (VPFP) equation on ℝ^3, a weighted C^m initial probability density, m≥3, with Gaussian velocity decay and polynomial spatial decay of order M>3 gives convergence to the global classical solution on every finite time interval. The proof combines conditioning of the initial product law with weighted BBGKY estimates. A decomposition of the potential and a bounded modification of the far-field force yield weighted bounds growing geometrically in the marginal order on the prescribed interval. A centered second-moment estimate permits summation of the error hierarchy, and a synchronous coupling transfers the estimate to the original dynamics.
ER -