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arXiv · 2509.17821

On the mean-field limit for the Vlasov-Poisson system in two dimensions

Manuela Feistl-Held·Peter Pickl
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Abstract

We present a probabilistic proof of the mean-field limit and propagation of chaos of a classical N-particle system in two dimensions with Coulomb interaction force of the form $f^N(q)=\pm\frac{q}{|q|^2}$ and $N$-dependent cut-off at $|q|>N^{-2}$. In particular, for typical initial data, we show convergence of the Newtonian trajectories to the characteristics of the Vlasov-Poisson system. The proof is based on a Gronwall estimate for the maximal distance between the exact microscopic dynamics and the approximate mean-field dynamics. Thus our result leads to a derivation of the Vlasov-Poisson equation from the microscopic $N$-particle dynamics with force term arbitrary close to the physically relevant Coulomb force.

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Manuela Feistl-Held, Peter Pickl. 2025-09-22. On the mean-field limit for the Vlasov-Poisson system in two dimensions. https://arxiv.org/abs/2509.17821

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