Propagation of chaos for topological interactions
File(s)Top_int_final1(1)(3).pdf (277.32 KB)
Accepted version
Author(s)
Degond, Pierre
Pulvirenti, Mario
Type
Journal Article
Abstract
We consider aN-particle model describing an alignment mechanism due to a topolog-ical interaction among the agents. We show that the kinetic equation, expected to holdin the mean-field limitN→∞, as following from the previous analysis in Ref. [3] can berigorously derived. This means that the statistical independence (propagation of chaos)is indeed recovered in the limit, provided it is assumed at time zero.
Date Issued
2019-07-23
Date Acceptance
2019-02-06
Citation
Annals of Applied Probability, 2019, 29 (4), pp.2594-2612
ISSN
1050-5164
Publisher
Institute of Mathematical Statistics
Start Page
2594
End Page
2612
Journal / Book Title
Annals of Applied Probability
Volume
29
Issue
4
Copyright Statement
© Institute of Mathematical Statistics, 2019.
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://projecteuclid.org/euclid.aoap/1563869051
Grant Number
WM130048
EP/M006883/1
EP/P013651/1
Subjects
Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Rank-based interactions
Boltzmann equation
BOLTZMANN-GRAD LIMIT
MEAN-FIELD LIMIT
GLOBAL VALIDITY
RARE-GAS
EQUATIONS
SYSTEMS
CONVERGENCE
PARTICLES
FLOCKING
FORCES
math-ph
math-ph
math.MP
Statistics & Probability
0102 Applied Mathematics
0104 Statistics
Publication Status
Published
Date Publish Online
2019-07-23