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Title: Graphon mean field systems
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.  more » « less
Award ID(s):
2106556
PAR ID:
10535683
Author(s) / Creator(s):
; ;
Publisher / Repository:
IMS
Date Published:
Journal Name:
The Annals of Applied Probability
Volume:
33
Issue:
5
ISSN:
1050-5164
Subject(s) / Keyword(s):
graphons, graphon particle systems, mean field interaction, heterogeneous interaction, networks, percolation
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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