4 papers
Derivation of 2D Vlasov-Poisson for classical particles with Coulomb interactions
Mitia Duerinckx, Pierre-Emmanuel Jabin
We obtain the first derivation of the 2D Vlasov-Poisson equation for classical particles with Coulomb interactions without any microscopic cutoff. The proof relies on our recent du…
Singular mean-field limits for fluctuations around equilibrium
Mitia Duerinckx, Pierre-Emmanuel Jabin
This work addresses the mean-field limit of inertial particle systems with singular interactions in a perturbative regime around Gibbs equilibrium. We prove that small fluctuations…
Kinetic theory for Transformers and the lost-in-the-middle phenomenon
Mitia Duerinckx, Borjan Geshkovski, Stefano Rossi
We study causal self-attention dynamics -- a toy model for decoder Transformers -- which we interpret as a non-exchangeable interacting particle system. Adapting cumulant expansion…
Correlation estimates for Brownian particles with singular interactions
Mitia Duerinckx, Pierre-Emmanuel Jabin
We study particle systems with singular pairwise interactions and non-vanishing diffusion in the mean-field scaling. A classical approach to describing corrections to mean-field be…