GRAPHON MEAN FIELD SYSTEMS

• 成果类型: Article
• 署名作者: Bayraktar, Erhan; Chakraborty, Suman; Wu, Ruoyu
• 署名单位: University of Michigan System; University of Michigan; Uppsala University; Iowa State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1901
• 发表日期: 2023
• 页码: 3587-3619
• 关键词: nonlinear heat-equation; l-p theory; interacting diffusions; models; CONVERGENCE; SEQUENCES

摘要

We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as the system size increases and the underlying graphons converge. The limit is given by a graphon mean field system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. Well-posedness, continuity and stability of such systems are provided. We also consider a not-so-dense analogue of the finite particle system, obtained by percolation with vanishing rates and suitable scaling of interactions. A law of large numbers result is proved for the convergence of such systems to the corresponding graphon mean field system.