Mean‐field limit of non‐exchangeable systems

This paper deals with the derivation of the mean‐field limit for multi‐agent systems on a large class of sparse graphs. More specifically, the case of non‐exchangeable multi‐agent systems consisting of non‐identical agents is addressed. The analysis does not only involve PDEs and stochastic analysis...

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Bibliographic Details
Published in:	Communications on pure and applied mathematics Vol. 78; no. 4; pp. 651 - 741
Main Authors:	Jabin, Pierre‐Emmanuel, Poyato, David, Soler, Juan
Format:	Journal Article
Language:	English
Published:	New York John Wiley and Sons, Limited 01.04.2025 Wiley
Subjects:	Graph theory Graphs Mathematics
ISSN:	0010-3640, 1097-0312
Online Access:	Get full text
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Summary:	This paper deals with the derivation of the mean‐field limit for multi‐agent systems on a large class of sparse graphs. More specifically, the case of non‐exchangeable multi‐agent systems consisting of non‐identical agents is addressed. The analysis does not only involve PDEs and stochastic analysis but also graph theory through a new concept of limits of sparse graphs (extended graphons) that reflect the structure of the connectivities in the network and has critical effects on the collective dynamics. In this article some of the main restrictive hypothesis in the previous literature on the connectivities between the agents (dense graphs) and the cooperation between them (symmetric interactions) are removed.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0010-3640 1097-0312
DOI:	10.1002/cpa.22235