# Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel

@article{Olivera2020QuantitativePA, title={Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel}, author={Christian Olivera and Alexandre Richard and Milica Toma{\vs}evi{\'c}}, journal={ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE}, year={2020} }

We propose a new approach to obtain quantitative convergence of moderately interacting
particle systems to solutions of nonlinear Fokker-Planck equations with singular kernels. Our
result only requires very weak regularity on the interaction kernel, including the Biot-Savart
kernel, the family of Keller-Segel kernels in arbitrary dimension, and more generally singular
Riesz kernels. This seems to be the first time that such quantitative convergence results are
obtained in Lebesgue and…

## 6 Citations

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. We show the weak convergence, up to extraction of a subsequence, of the empirical measure for the Keller-Segel system of particles in both subcritical and critical cases. We use a simple two…

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Abstract A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole…

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