2016/01/05 by Tanguy Cabana, Jonathan Touboul, Cabana, Tanguy +1
Computer Science · Mathematics · Neuroscience · #FOS: Mathematics #Functional Brain Connectivity Studies #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1601.00985
openalex publication_date 2016/01/05 · arxiv created 2017/01/04 · arxiv updated 2017/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work continues the analysis of large deviations for randomly connected neural networks models of the brain. The originality of the model relies on the fact that the directed impact of one particle onto another depends on the state of both particles, and (ii) have random Gaussian amplitude with mean and variance scaling as the inverse of the network size. Similarly to the spatially extended case, we show that under sufficient regularity assumptions, the empirical measure satisfies a large-deviation principle with good rate function achieving its minimum at a unique probability measure, implying in particular its convergence in both averaged and quenched cases, as well as a propagation of chaos property (in the averaged case only). The class of model we consider notably includes a stochastic version of Kuramoto model with random connections.