A family of interacting particle systems pinned to their ensemble average. (4th October 2021)

• Record Type: Journal Article
• Authors: Mengütürk, Levent Ali
• Is Part Of: Journal of physics. Volume 54:Number 43(2021)
• Publication Date: 2021-10-04
• Subjects: interacting particle systems -- pinned diffusions -- mean-field analysis; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac2715
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We study a family of interacting particle diffusions that converge to their random ensemble-average at some fixed future time for any given number of elements in the system. We impose certain conditions on a class of differential equations that model particle dynamics which are influenced by the average statistic of the whole system. As such, these processes achieve mean-field limits when the number of particles increase asymptotically, whereby the iterated limits over time vs the number of units are commutative. In a specific case, we show that the mean-field limit of the system consists of mutually independent α -Wiener bridges, instead of Ornstein–Uhlenbeck processes typically seen in the classical setting. We provide examples with simulations for demonstration.