Dear Colleagues,
We would like to invite you to the following SPASS seminar, jointly organized by UniPi, SNS, UniFi and UniSi: *Quantitative particle approximation of nonlinear stochastic Fokker-Planck equations with singular kernel* by Josué Knorst (ENSTA-Paris, UNICAMP)
The seminar will take place TUE, 4.2.2025 at 14:00 CET in Aula Magna, Dipartimento di Matematica, UNIPI and streamed online at the link below.
The organizers, G. Bet, A. Caraceni, F. Grotto, G. Zanco https://sites.google.com/unipi.it/spass
*---------------------------------------------------------* *Abstract: * We derive quantitative estimates for stochastic systems of particles moderately interacting via singular kernels and perturbed by both idiosyncratic and environmental noises. The moderate interaction regime is a scale introduced by Oelschläger in the 80s, and it lies between the mean field and the nearest neighbor interaction regimes. We prove that the (mollified) empirical process converges to the solution of the nonlinear stochastic Fokker-Planck equation. The proof is based on Itô’s formula for the norm of a H^1_q-valued process, commutator estimates, and some estimations for the regularization of the empirical measure. Joint work with C. Olivera and A. de Souza.