Work

Propagation of Chaos for Point Processes Induced by Particle Systems with Mean-Field Drift Interaction

Year: 2024

Type: article

Abstract: We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: It has the same weak limit as the point process induced by i.i.d. copies of the solution of a limiting McKean–Vlasov equation. This weak limit is a Poisson point process whose intensity measure is related to classical extreme value distributions. In particular, this yields the limiting distribution of the normalized upper order statistics.

Source: Journal of Theoretical Probability

DOI: 10.1007/s10959-024-01397-3

Authors: Nikolaos Kolliopoulos, Martin Larsson, Zeyu Zhang

Institutions: University of Michigan, Carnegie Mellon University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: National Science Foundation, Carnegie Mellon University