Inspired by neuronal integrate-and-fire models, Chariker and Lebowitz introduced an interacting particle system which they called the mean-field generalized contact process. In this model, neurons are placed on the vertices of a lattice, and they have an integer-valued voltage. When this voltage attains a threshold k, the neuron becomes active and induces the activation of other neurons, mediated by an interaction kernel J. Active neurons become inactive at an exponential rate a. This informal description can be modeled by a Markov chain: the aforementioned mean-field generalized contact process. Together with Anna de Masi and Errico Presutti, the authors derived the hydrodynamic equation of this model, namely, they showed that the empirical density of voltage values converges to the solution of a PDE of mean-field type. This result can be understood as a law of large numbers, and our aim is to derive a quantitative version of this law of large numbers, as well as the corresponding central limit theorem.

Joint work with Julian Amorim and Yangrui Xiang (IMPA)

Texto informado pelo autor.

* Os participantes dos seminários não poderão acessar às dependências da FGV usando bermuda, chinelos, blusa modelo top ou cropped, minissaia ou camiseta regata. O uso da máscara é facultativo, porém é obrigatória a apresentação do comprovante de vacinação (físico ou digital).