Probabilistic estimates for a system of noisy integrate-and-fire neurons

Ben Hambly; Aldaïr Petronilia; Christoph Reisinger; Andreas Søjmark

Probabilistic estimates for a system of noisy integrate-and-fire neurons

Probability 2026-07-10 v1

Authors: Ben Hambly , Aldaïr Petronilia , Christoph Reisinger , Andreas Søjmark

Abstract

In this note, we establish various probabilistic estimates for an interacting particle system that describes the evolution of the membrane potentials in a network of excitatory integrate-and-fire neurons, which are subject to both idiosyncratic and common noise. These estimates serve to support a separate work that studies the large population limit and the corresponding stochastic Fokker--Planck equation for the membrane potential density.

Keywords

integrate-and-fire neurons interacting particle systems probabilistic estimates common noise idiosyncratic noise Fokker-Planck equation

Cite

@article{arxiv.2607.09575,
  title  = {Probabilistic estimates for a system of noisy integrate-and-fire neurons},
  author = {Ben Hambly and Aldaïr Petronilia and Christoph Reisinger and Andreas Søjmark},
  journal= {arXiv preprint arXiv:2607.09575},
  year   = {2026}
}

Comments

27 pages