@unpublished{Feistl-HeldPickl2025,
  author    = {Feistl-Held, Manuela and Pickl, Peter},
  title     = {On the mean-field limit for the Vlasov-Poisson system in two dimensions},
  doi       = {10.48550/arXiv.2509.17821},
  institution = {Fakult{\"a}t f{\"u}r Angewandte Natur- und Geisteswissenschaften},
  year      = {2025},
  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.},
  language  = {en}
}