We rigorously prove a central limit theorem for neural network models with a single hidden
layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) …

We consider the asymptotic behaviour of the fluctuations for the empirical measures of
interacting particle systems with singular kernels. We prove that the sequence of fluctuation …

In the present work, we introduce a general class of mean-field interacting nonlinear
Hawkes processes modeling the reciprocal interactions between two neuronal populations …

We study a multivariate, non-linear Hawkes process ZN on the complete graph with N
nodes. Each vertex is either excitatory (probability p) or inhibitory (probability 1− p). We take …

Can we use spiking neural networks (SNN) as generative models of multi-neuronal
recordings, while taking into account that most neurons are unobserved? Modeling the …

Population equations for infinitely large networks of spiking neurons have a long tradition in
theoretical neuroscience. In this work, we analyze a recent generalization of these equations …

We investigate the asymptotic behavior of networks of interacting non-linear Hawkes
processes modeling a homogeneous population of neurons in the large population limit. In …

We study an individual-based stochastic epidemic model in which infected individuals
become susceptible again following each infection. In contrast to classical compartment …

In a previous paper Chevallier et al.(2018), it has been shown that the mean-field limit of
spatially extended Hawkes processes is characterized as the unique solution u (t, x) of a …

Hawkes processes are a class of simple point processes whose intensity depends on the
past history, and is in general non-Markovian. Limit theorems for Hawkes processes in …