2020/08/24 by Erhan Bayraktar, Ruoyu Wu, Bayraktar, Erhan +1 · 2 citations
Mathematics · #05C80 #60J60 #60K35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2008.10173
openalex publication_date 2020/08/24 · openalex created_date 2022/10/09 · openalex updated_date 2026/07/28
We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by a graphon particle system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Under suitable assumptions, including a certain convexity condition, we show the exponential ergodicity for both systems, establish the uniform-in-time law of large numbers for marginal distributions as the number of particles increases, and introduce the uniform-in-time Euler approximation. The precise rate of convergence of the Euler approximation is provided.