Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane
Offered By: Institut des Hautes Etudes Scientifiques (IHES) via YouTube
Course Description
Overview
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.
Syllabus
Milica Tomašević - Particle Approximation of the Doubly Parabolic Keller-Segel Equation in the Plane
Taught by
Institut des Hautes Etudes Scientifiques (IHES)
Related Courses
Introduction to Statistics: ProbabilityUniversity of California, Berkeley via edX Aléatoire : une introduction aux probabilités - Partie 1
École Polytechnique via Coursera Einführung in die Wahrscheinlichkeitstheorie
Johannes Gutenberg University Mainz via iversity Combinatorics and Probability
Moscow Institute of Physics and Technology via Coursera Probability
University of Pennsylvania via Coursera