Abstract
The Keller Segel particle system describes N plantar Brownians interacting via an attractive force in 1/r, where r denotes the distance between the particles. One of the main difficulties and original features of this system is that the particles can collide with each other, rendering the drift ill-defined.
Existence for this system has already been shown up to the time of the first collision between three particles in Fournier-Jourdain (2017), and in a weaker sense via Dirichlet shape theory in Fournier-Tardy (2022), for almost all initial conditions only.
This work-in-progress explains how to extend the decomposition introduced in Fournier-Tardy (2022) into an excursion theory for this particle system. This new understanding of the process allows us to define a solution via a generalized EDS invoking principal values in the drift and to prove uniqueness in law. Other consequences of the decomposition will be presented if time permits.
