Schmutz, Valentin2022-05-232022-05-232022-05-232022-07-0110.1016/j.spa.2022.03.006https://infoscience.epfl.ch/handle/20.500.14299/187967WOS:000792916500002We propose a mean-field model of interacting point processes where each process has a memory of the time elapsed since its last event (age) and its recent past (leaky memory), generalizing Age-dependent Hawkes processes. The model is motivated by interacting nonlinear Hawkes processes with Markovian self-interaction and networks of spiking neurons with adaptation and short-term synaptic plasticity. By proving propagation of chaos and using a path integral representation for the law of the limit process, we show that, in the mean-field limit, the empirical measure of the system follows a (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Statistics & ProbabilityMathematicshawkes processmean-field approximationnonlocal transport equationpropagation of chaoserlangkernelshort-term synaptic plasticityspiking neuronsfunctional connectivitynetworkmodelpopulationspropagationdynamicstext::journal::journal article::research article