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

Probability Seminar

4th March 2022, 3:30 pm – 4:30 pm

Fry Building, 2.04 (also on zoom)

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.

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