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

Ben Hambly; Aldaïr Petronilia; Christoph Reisinger; Andreas Søjmark

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arXiv · 2607.09575

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

Ben Hambly·Aldaïr Petronilia·Christoph Reisinger·Andreas Søjmark

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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.

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Ben Hambly, Aldaïr Petronilia, Christoph Reisinger, Andreas Søjmark. 2026-07-10. Probabilistic estimates for a system of noisy integrate-and-fire neurons. https://arxiv.org/abs/2607.09575

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