The mean-field limit of sparse networks of integrate-and-fire neurons
Year: 2025
Type: article
Abstract: We study the mean-field limit of a model of biological neuron networks based on the so-called stochastic integrate-and-fire (IF) dynamics. However, we do not assume any structure on the graph of interactions but consider instead any connection weights between neurons that obey a generic mean-field scaling. To address this, we propose a novel notion of observables that naturally extends the marginals laws in studying classical many-particle systems. We prove the stability of the network in terms of observables, by applying a novel commutator estimate in weak norms to a tree-indexed extension of the BBGKY hierarchy. While we require non-vanishing diffusion, this approach notably addresses the challenges of sparse interacting graphs/matrices and singular interactions from Poisson jumps, and requires no additional regularity on the initial distribution.
DOI: 10.4171/aihpc/157
Authors: Pierre-Emmanuel Jabin, Datong Zhou
Institutions: Pennsylvania State University, Sorbonne Université
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $700
OpenAlex ID: W4411429513