Nonlinear Graphon mean-field systems
arxiv(2024)
摘要
We address a system of weakly interacting particles where the heterogenous
connections among the particles are described by a graph sequence and the
number of particles grows to infinity. Our results extend the existing law of
large numbers and propagation of chaos results to the case where the
interaction between one particle and its neighbors is expressed as a nonlinear
function of the local empirical measure. In the limit of the number of
particles which tends to infinity, if the graph sequence converges to a
graphon, then we show that the limit system is described by an infinite
collection of processes and can be seen as a process in a suitable L^2 space
constructed via a Fubini extension. The proof is built on decoupling techniques
and careful estimates of the Wasserstein distance.
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