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Title: Propagation of chaos for maxima of particle systems with mean-field drift interaction
Abstract We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as those arising in an i.i.d. system where each particle follows the associated McKean–Vlasov limiting dynamics. Because the maximum depends on all particles, our result does not follow from classical propagation of chaos, where convergence to an i.i.d. limit holds for any fixed number of particles but not all particles simultaneously. The proof uses a change of measure argument that depends on a delicate combinatorial analysis of the iterated stochastic integrals appearing in the chaos expansion of the Radon–Nikodym density.  more » « less
Award ID(s):
2206062
PAR ID:
10425190
Author(s) / Creator(s):
; ;
Publisher / Repository:
Springer Science + Business Media
Date Published:
Journal Name:
Probability Theory and Related Fields
Volume:
187
Issue:
3-4
ISSN:
0178-8051
Format(s):
Medium: X Size: p. 1093-1127
Size(s):
p. 1093-1127
Sponsoring Org:
National Science Foundation
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