Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane

Explore a 50-minute conference talk on the particle approximation of the doubly parabolic Keller-Segel equation in the plane. Delve into the study of a stochastic system of N particles associated with the parabolic-parabolic Keller-Segel system, examining its singular and non-Markovian nature. Learn about the existence of this particle system for N≥2 when the sensitivity parameter is sufficiently small, and discover the tightness in N of its empirical measure. Investigate how any weak limit point of this empirical measure, as N approaches infinity, solves a nonlinear martingale problem and how its family of time-marginals solves the parabolic-parabolic Keller-Segel system in a weak sense. Understand the main argument of the proof, which involves a "Markovianization" of the interaction kernel, demonstrating how the two-by-two path-dependent interaction can be controlled by a two-by-two Coulomb interaction. This talk, presented by Milica Tomašević from CNRS & École polytechnique, is based on joint work with N. Fournier from Sorbonne Université.