Conditional propagation of chaos for interacting particle systems with stable jumps
par
Eva Löcherbach(Université Paris 1 Panthéon Sorbonne)
→
Europe/Paris
Lyon 1
Lyon 1
Description
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.