Some stochastic particle systems models of neuronal networks

Neuronal networks may be represented as stochastic particle systems. Every particle has an associated potential and the dynamics of the potential of each particle is described by some stochastic differential equations. In works by Delarue, Inglis, Rubenthaler and Tanré a complete graph has been considered as a model of the neurons of the human brain and its solution has been shown to converge to a mean-field limit stochastic differential equation. We first introduce those results, later moving to a discussion of possible alternative models which would better represent the topology of the human brain, according to empirical observations