RT Journal Article
SR 00
ID 10.1007/s10955-017-1882-z
A1 Blanchet, Adrien
A1 Degond, Pierre
T1 Kinetic models for topological nearest-neighbor interactions
JF Journal of Statistical Physics
YR 2017
FD 2017-12
VO 169
IS 5
SP 929
OP 950
K1 rank-based interaction
K1 spatial diffusion equation
K1 continuity equation
K1 concentration of measure
AB We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal and human behavior. Precisely, the system consists of a finite number of particles characterized by their positions and velocities. At random times a randomly chosen particle, the follower adopts the velocity of its closest neighbor, the leader. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit kinetic equation is a non-standard spatial diffusion equation for the particle distribution function. We also study the case wherein the particles interact with their K closest neighbors and show that the corresponding kinetic equation is the same. Finally, we prove that these models can be seen as a singular limit of the smooth rank-based model previously studied in [10]. The proofs are based on a combinatorial interpretation of the rank as well as some concentration of measure arguments.
PB Kluwer
SN 1572-9613
LK https://publications.ut-capitole.fr/id/eprint/25738/
UL http://tse-fr.eu/pub/32176