Giovanni Brigati - Kinetic Optimal Transport скачать в хорошем качестве

Giovanni Brigati - Kinetic Optimal Transport

This lecture was part of the Workshop on "Probabilistic Mass Transport - from Schrödinger to Stochastic Analysis" held at the ESI February 9 - 13, 2026. In this talk, I will present the recent work on Kinetic Optimal Transport, due to Jan Maas, Filippo Quattrocchi, and myself. I introduce our construction, with the definition of a second-order kinetic discrepancy between probability measures on the phase space, based on Newton's equations. Then, I focus on the proof of our main result: absolutely continuous curves of measures in the kinetic setting are in a one-to-one correspondence with solutions to Vlasov's equations.