Replica mean-field (RMF) models have been introduced in various fields (biological neural networks, telecommunication networks) to study limit behaviors in models whilst preserving the finite-size effects of interactions inside the considered networks. Replica-mean-field models are made of infinitely many replicas which interact according to the same basic structure as that of the finite network of interest.
I will present the RMF structure in discrete time in a very general setting and show properties that arise at the limit in the number of replicas, such as asymptotic independence between replicas and the asymptotic behavior of the arrivals process to a given replica. I will also present RMF models in continuous time which are of particular interest in computational neuroscience.