Eva Löcherbach

Conditional propagation of chaos for interacting particle systems in a diffuse regime

This is a joint work with Xavier Erny and Dasha Loukianova.
We consider interacting particle systems which are mainly inspired by stochastic models of spiking neurons, in a diffusive scaling. The system consists of N particles, each jumping randomly with rate depending on its state.
At its jump time, the state of the jumping particle is reset to a given value (which is the resting potential for neurons) and all other particles
receive a centered random quantity which is added to their state variable. In between successive spikes, each particle follows a
deterministic flow. I first briefly discuss the convergence of the system, as the system size diverges, to a limit nonlinear
jumping stochastic differential equation. Then I will show how to establish a strong convergence result, stated with respect to an appropriate distance, with an explicit rate of convergence. The main technical ingredient of the proof is the coupling introduced in Komlos-Major-Tusnady (1975) of the point process representing the small jumps of the particle system with the limit Brownian motion.