Tootfinder

Non-exchangeable mean-field theory for adaptive weights: propagation of chaos and graphon sampling lemma
Datong Zhou
https://arxiv.org/abs/2506.13587 https…

Non-exchangeable mean-field theory for adaptive weights: propagation of chaos and graphon sampling lemma
We develop a mean-field theory for large, non-exchangeable particle (agent) systems where the states and interaction weights co-evolve in a coupled system of SDEs. A first main result is a generalization of the propagation of chaos. The weight adaptation in the SDEs makes the classical approach of using a static probability space as the continuum limit for the agent labels inadequate. We address this by introducing a label space endowed with a filtration that captures the stochasticity. While t…

Adaptive Cucker-Smale Networks: Limiting Laplacian Time-Varying Dynamics
Christian Kuehn, Jaeyoung Yoon
https://arxiv.org/abs/2506.06131 https://

Adaptive Cucker-Smale Networks: Limiting Laplacian Time-Varying Dynamics
Differences in opinion can be seen as distances between individuals, and such differences do not always vanish over time. In this paper, we propose a modeling framework that captures the formation of opinion clusters, based on extensions of the Cucker Smale and Hegselmann Krause models to a combined adaptive (or co-evolutionary) network. Reducing our model to a singular limit of fast adaptation, we mathematically analyze the asymptotic behavior of the resulting Laplacian dynamics over various c…