PROPAGATION OF CHAOS AND THE MANY-DEMES LIMIT FOR WEAKLY INTERACTING DIFFUSIONS IN THE SPARSE REGIME

• 成果类型: Article
• 署名作者: Hutzenthaler, Martin; Pieper, Daniel
• 署名单位: University of Duisburg Essen
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1559
• 发表日期: 2020
• 页码: 2311-2354
• 关键词: large numbers; converge; LAW

摘要

Propagation of chaos is a well-studied phenomenon and shows that weakly interacting diffusions may become independent as the system size converges to infinity. Most of the literature focuses on the case of exchangeable systems where all involved diffusions have the same distribution and are of the same size. In this paper, we analyze the case where only a few diffusions start outside of an accessible trap. Our main result shows that in this sparse regime the system of weakly interacting diffusions converges in distribution to a forest of excursions from the trap. In particular, initial independence propagates in the limit and results in a forest of independent trees.