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October 2020 Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regime
Martin Hutzenthaler, Daniel Pieper
Ann. Appl. Probab. 30(5): 2311-2354 (October 2020). DOI: 10.1214/20-AAP1559

Abstract

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.

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Martin Hutzenthaler. Daniel Pieper. "Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regime." Ann. Appl. Probab. 30 (5) 2311 - 2354, October 2020. https://doi.org/10.1214/20-AAP1559

Information

Received: 1 April 2018; Revised: 1 May 2019; Published: October 2020
First available in Project Euclid: 15 September 2020

MathSciNet: MR4149530
Digital Object Identifier: 10.1214/20-AAP1559

Subjects:
Primary: 60K35
Secondary: 60J70, 92D25

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 5 • October 2020
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