Conditional propagation of chaos for interacting particle systems with stable jumps

par Eva Löcherbach (Université Paris 1 Panthéon Sorbonne)

jeudi 1 févr. 2024, 14:00 → 15:00 Europe/Paris

Lyon 1

We consider systems of particles taking values in R with mean field interactions. Each particle jumps at a rate depending on its position. When jumping it gives a random quantity to each of the other particles (collateral jumps) while its own position undergoes a main jump.

This model is inspired by neuroscience (particles being the neurons which are represented by their membrane potential and collateral jumps being the synaptic weight of a pre- on a post-synaptic neuron).

I will concentrate on the study of the case when the collateral jumps are random variables that belong to the domain of attraction of a stable law.

In a first part of the talk I will discuss the mean field limits of such systems and explain the precise form of the limit equation which is due to a stable limit theorem.

I will then show how to use a coupling approach to obtain a strong rate of convergence for the associated (conditional) propagation of chaos result.

This is a joint work with Dasha Loukianova.