Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics



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BibTex format

author = {Blanchet, A and Degond, PAA},
doi = {10.1007/s10955-017-1882-z},
journal = {Journal of Statistical Physics},
pages = {929--950},
title = {Kinetic models for topological nearest-neighbor interactions},
url = {},
volume = {169},
year = {2017}

RIS format (EndNote, RefMan)

AB - We consider systems of agents interacting through topological interactions. Thesehave been shown to play an important part in animal and human behavior. Precisely, thesystem 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 closestneighbor, the leader. We study the limit of a system size going to infinity and, under theassumption of propagation of chaos, show that the limit kinetic equation is a non-standardspatial diffusion equation for the particle distribution function. We also study the case whereinthe particles interact with their K closest neighbors and show that the corresponding kineticequation is the same. Finally, we prove that these models can be seen as a singular limitof the smooth rank-based model previously studied in Blanchet and Degond (J Stat Phys163:41–60, 2016). The proofs are based on a combinatorial interpretation of the rank as wellas some concentration of measure arguments.
AU - Blanchet,A
AU - Degond,PAA
DO - 10.1007/s10955-017-1882-z
EP - 950
PY - 2017///
SN - 1572-9613
SP - 929
TI - Kinetic models for topological nearest-neighbor interactions
T2 - Journal of Statistical Physics
UR -
UR -
VL - 169
ER -